{"id":55,"date":"2022-12-19T17:49:56","date_gmt":"2022-12-19T22:49:56","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math024\/chapter\/rounding-numbers\/"},"modified":"2025-07-15T22:25:07","modified_gmt":"2025-07-16T02:25:07","slug":"rounding-numbers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math024\/chapter\/rounding-numbers\/","title":{"raw":"Topic D: Rounding Numbers","rendered":"Topic D: Rounding Numbers"},"content":{"raw":"If a pair of jeans cost $49.98, what amount would you say if someone asks what you paid for them? You would probably say, \"They cost around $50.\"\r\n\r\nWe often round cents to dollars as we go about our lives. You may already have an idea of how to do this. For example, answer these questions.\r\n<ul>\r\n \t<li>About how much do your groceries cost each month?<\/li>\r\n \t<li>About how much does it cost to fill a small car's gas tank?<\/li>\r\n<\/ul>\r\nLook at your answers. The amount for groceries may be quite large. When you estimated your answer, how did you round the amount? For example, if your real monthly grocery bill was $481.73 you might have said $482 or perhaps $480.\u00a0 Perhaps you even have estimated to the nearest hundred dollars and said, \"About $500 a month for groceries.\" All those estimates would be correct.\r\n<div class=\"textbox\">\r\n\r\nThe amount for a tank of gas is less than a month's groceries. How did you estimate?\r\n\r\nFor example, a small car may take $54.72 of gas.\r\n<p class=\"indent\">If you estimated to the nearest dollar, you would say, \"About $55.\"<\/p>\r\n<p class=\"indent\">If you estimated to the nearest ten dollars, you would say, \"About $50.\"<\/p>\r\n<p class=\"indent\">If you rounded to the nearest dollar you would say, \"54 dollars.\"<\/p>\r\n\r\n<\/div>\r\nWe round a number in different ways depending on several things:\r\n<ul>\r\n \t<li>the size of the number we are rounding<\/li>\r\n \t<li>what we are going to do with the number after we have rounded it off<\/li>\r\n \t<li>our own convenience<\/li>\r\n<\/ul>\r\nCarefully review the [pb_glossary id=\"200\"]place value[\/pb_glossary] for whole numbers.\r\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<th style=\"text-align: center\" colspan=\"3\" scope=\"col\">Thousands<\/th>\r\n<th class=\"shaded\" style=\"text-align: center\" colspan=\"3\" scope=\"col\">Ones<\/th>\r\n<th scope=\"col\"><\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 14%;text-align: center\" scope=\"col\">Hundred thousands<\/td>\r\n<td style=\"width: 14%;text-align: center\" scope=\"col\">Ten thousands<\/td>\r\n<td style=\"width: 14%;text-align: center\" scope=\"col\">One thousand<\/td>\r\n<td class=\"shaded\" style=\"width: 14%;text-align: center\" scope=\"col\">Hundreds<\/td>\r\n<td class=\"shaded\" style=\"width: 14%;text-align: center\" scope=\"col\">Tens<\/td>\r\n<td class=\"shaded\" style=\"width: 14%;text-align: center\" scope=\"col\">Ones<\/td>\r\n<td style=\"width: 14%;text-align: center\" scope=\"col\">Decimal<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Rounding Whole Numbers<\/h1>\r\nWe round <strong>down<\/strong> if the [pb_glossary id=\"169\"]digit[\/pb_glossary] to the right is less than 5. We round <strong>up<\/strong> if the digit to the right is 5 or more.\r\n<ul>\r\n \t<li>Rounding numbers gives an approximate amount; it is not an accurate figure.<\/li>\r\n \t<li>Use a different form of the equal sign (\u2248) which means \u201capproximate equality.\u201d<\/li>\r\n<\/ul>\r\n<h2>Review: Rounding to the Nearest Ten<\/h2>\r\n<ul>\r\n \t<li>Underline the tens digit<\/li>\r\n \t<li>Look at the digit in the ones place (to the right). You can put an arrow above it to help you find it later.\r\n<ul>\r\n \t<li>If the ones digit is <strong>5 or more, round up<\/strong>. Write the ones digit as zero and increase the tens digit by one.<\/li>\r\n \t<li>If the ones digit is <strong>less than 5, round down<\/strong>. The tens digit does not change and the ones digit is written as a zero.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n\u00a0[latex]\\begin{array}{r}\\downarrow\\\\\\underline{2}3\\end{array}[\/latex]\r\n\r\n23 is rounded down to 20. The tens digit stays the same.\r\n\r\n23 \u2248 20\r\n\r\n<\/div>\r\n<\/div>\r\nHere's another example:\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}{r}\\downarrow\\\\2\\underline{8}7\\end{array}[\/latex]\r\n\r\n287 is rounded up to 290. The tens digit increases by 1.\r\n\r\n287 \u2248 290.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound each of the following to the nearest ten. Use the \u201capproximate equality\u201d sign \u2248.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>46 \u2248 50<\/li>\r\n \t<li>111 \u2248 110<\/li>\r\n \t<li>7 \u2248<\/li>\r\n \t<li>116 \u2248<\/li>\r\n \t<li>71 \u2248<\/li>\r\n \t<li>89 \u2248<\/li>\r\n \t<li>96 \u2248<\/li>\r\n \t<li>4 \u2248<\/li>\r\n \t<li>385 \u2248<\/li>\r\n \t<li>108 \u2248<\/li>\r\n \t<li>73 \u2248<\/li>\r\n \t<li>17 \u2248<\/li>\r\n \t<li>361 \u2248<\/li>\r\n \t<li>8 \u2248<\/li>\r\n \t<li>49 \u2248<\/li>\r\n \t<li>148 \u2248<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>50<\/li>\r\n \t<li>110<\/li>\r\n \t<li>10<\/li>\r\n \t<li>120<\/li>\r\n \t<li>70<\/li>\r\n \t<li>90<\/li>\r\n \t<li>100<\/li>\r\n \t<li>0<\/li>\r\n \t<li>390<\/li>\r\n \t<li>110<\/li>\r\n \t<li>70<\/li>\r\n \t<li>20<\/li>\r\n \t<li>360<\/li>\r\n \t<li>10<\/li>\r\n \t<li>50<\/li>\r\n \t<li>150<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h2>Review: Rounding to the Nearest Hundred<\/h2>\r\n<ul>\r\n \t<li>Underline the hundreds digit.<\/li>\r\n \t<li>Look at the digit in the tens place (to the right). You can put an arrow above it to help you find it later.\r\n<ul>\r\n \t<li>If the tens digit is <strong>5 or more, round up<\/strong>. Write the tens and ones digit as zero and increase the hundreds digit by one.<\/li>\r\n \t<li>If the tens digit is <strong>less than 5, round down<\/strong>. The hundreds digit does not change and the tens and ones digit is written as a zero.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example C<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n\u00a0[latex]\\begin{array}{c}\\downarrow\\\\ \\underline{4}73\\end{array}[\/latex]\r\n\r\n473 is rounded up to 500.\r\n\r\n473 \u2248 500\r\n\r\n<\/div>\r\n<\/div>\r\nRound down if the tens digit is less than 5 and up if it is 5 or more:\r\n<ul>\r\n \t<li>728 rounded to the nearest hundred is 700. (The tens digit is 2, which is less than 5, so the hundreds digit stays the same.)<\/li>\r\n \t<li>758 rounded to the nearest hundred is 800. (The tens digit is 5, which is five or more, so the hundreds digit increases by 1.)<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound each of the following to the nearest HUNDRED. Use the \u201capproximate equality\u201d sign \u2248.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>330\u00a0 \u2248\u00a0 300<\/li>\r\n \t<li>908<\/li>\r\n \t<li>2795<\/li>\r\n \t<li>1260<\/li>\r\n \t<li>742<\/li>\r\n \t<li>127<\/li>\r\n \t<li>302<\/li>\r\n \t<li>945<\/li>\r\n \t<li>865<\/li>\r\n \t<li>275<\/li>\r\n \t<li>590<\/li>\r\n \t<li>1240<\/li>\r\n \t<li>214<\/li>\r\n \t<li>4450<\/li>\r\n \t<li>98<\/li>\r\n \t<li>996<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>300<\/li>\r\n \t<li>900<\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">800<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">300<\/span><\/li>\r\n \t<li>700<\/li>\r\n \t<li>100<\/li>\r\n \t<li>300<\/li>\r\n \t<li>900<\/li>\r\n \t<li>900<\/li>\r\n \t<li>300<\/li>\r\n \t<li>600<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">200<\/span><\/li>\r\n \t<li>200<\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">500<\/span><\/li>\r\n \t<li><span style=\"margin-left: 0.25em\">100<\/span><\/li>\r\n \t<li><span style=\"margin-left: 0.25em\">1<span style=\"margin-left: 0.25em\">000<\/span><\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h2>Review: Rounding to the Nearest Thousand<\/h2>\r\n<ul>\r\n \t<li>Underline the thousands digit<\/li>\r\n \t<li>Look at the digit in the hundreds place (to the right). You can put an arrow above it to help you find it later.\r\n<ul>\r\n \t<li>If the hundreds digit is <strong>5 or more, round up<\/strong>. Write the hundreds, tens and ones digit as zero and increase the thousands digit by one.<\/li>\r\n \t<li>If the hundreds digit is <strong>less than 5, round down<\/strong>. The thousands digit does not change and the hundreds, tens and ones digit is written as a zero.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example D<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}{l}\\hspace{0.5em}\\downarrow\\\\ \\underline{3}485\\end{array}[\/latex]\r\n\r\n3<span style=\"margin-left: 0.25em\">485<\/span> is rounded down to 3<span style=\"margin-left: 0.25em\">000<\/span>.\r\n\r\n3<span style=\"margin-left: 0.25em\">485<\/span> \u2248 3<span style=\"margin-left: 0.25em\">000<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\nRound down if the hundreds digit is less than 5 and round up if it is 5 or more:\r\n<ul>\r\n \t<li>2<span style=\"margin-left: 0.25em\">109<\/span> rounded to the nearest thousand is 2<span style=\"margin-left: 0.25em\">000<\/span>. (The hundreds digit is 1, which is less than 5.)<\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">643<\/span> rounded to the nearest thousand is 3<span style=\"margin-left: 0.25em\">000<\/span>. (The hundreds digit is 6, which is more than 5.)<\/li>\r\n \t<li>0940 rounded to the nearest thousand is 1<span style=\"margin-left: 0.25em\">000<\/span>. (The hundreds digit is 9, which is more than 5, so the thousands digit increases from 0 to 1.)<\/li>\r\n \t<li>0465 rounded to the nearest thousand is 0. (The hundreds digit is 4, which is less than 5, so the thousands digit stays at 0.)<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound each of the following to the nearest thousand. Use the \u201capproximate equality\u201d sign \u2248.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>1<span style=\"margin-left: 0.25em\">760<\/span>\u00a0 \u2248\u00a0 2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">250<\/span><\/li>\r\n \t<li>850\u00a0<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/li>\r\n \t<li>320<\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em\">544<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">234\u00a0<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span><\/li>\r\n \t<li>492<\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">199<\/span><\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em\">883<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">045<\/span><\/li>\r\n \t<li>7<span style=\"margin-left: 0.25em\">856<\/span><\/li>\r\n \t<li>500<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">780<\/span><\/li>\r\n \t<li>495<\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em\">300<\/span><\/li>\r\n \t<li>700<\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">449<\/span><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em\">555<\/span><\/li>\r\n \t<li>8<span style=\"margin-left: 0.25em\">914<\/span><\/li>\r\n \t<li>85<span style=\"margin-left: 0.25em\">455<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">475\u00a0<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span><\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>0<\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li><span style=\"margin-left: 0.25em\">0<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>10<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>8<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>0<\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>85<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Rounding Decimals to Whole Numbers<\/h1>\r\nRemember, decimals are part of the whole thing. We can round the decimal to the nearest whole number. Rounding to whole numbers means rounding off to the ones place.\r\n\r\nWhen rounding to the whole number:\r\n<ul>\r\n \t<li>Underline the ones digit<\/li>\r\n \t<li>Look at the digit in the thenths place (to the right). You can put an arrow above it to help you find it later.\r\n<ul>\r\n \t<li>If the tenths digit is <strong>5 or more, round up<\/strong>. Increase the ones digit by one. Do not write a decimal or any decimal digits.<\/li>\r\n \t<li>If the tenths digit is <strong>less than 5, round down<\/strong>. The ones digit does not change. Do not write a decimal or any decimal digits,<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example E<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\begin{array}{l}\\hspace{1.3em}\\downarrow\\\\ 3\\underline{7}.482\\end{array}[\/latex]\r\n\r\n37.482 rounded to the nearest whole number is 37. (The tenths digit is 4, which is less than 5.)\r\n\r\n37.482 \u2248 37\r\n\r\n[latex]\\begin{array}{l}\\hspace{1.3em}\\downarrow\\\\ 3\\underline{7}.906\\end{array}[\/latex]\r\n\r\n37.906\u00a0 rounded to the nearest whole number is 38. (The tenths digit is 9, which is more than 5.)\r\n\r\n37. 906 \u2248 38\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example F<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol>\r\n \t<li>Round to a whole number.\r\n[latex]\\begin{array}{l}\\hspace{5.58em}\\downarrow\\\\ 42.123\\rightarrow4\\underline{2}.123\\approx42\\end{array}[\/latex]<\/li>\r\n \t<li>Round 960.802 to the nearest whole number.\r\n[latex]\\begin{array}{l}\\hspace{6.6em}\\downarrow\\\\ 960.802\\rightarrow96\\underline{0}.802\\approx961\\end{array}[\/latex]<\/li>\r\n \t<li>Round 39.5 to the nearest ones.\r\n[latex]\\begin{array}{l}\\hspace{4.6em}\\downarrow\\\\ 39.5\\rightarrow3\\underline{9}.5\\approx40\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">\r\n\r\n<strong>Z<\/strong><strong>e<\/strong><strong>r<\/strong><strong>os again \u2013 <\/strong>\r\n\r\nYou know that zeros at the end of a decimal do not change the value of the amount. You can add as many as you like.\r\n\r\nBut when a decimal has been rounded, drop any zeros after the place where you have rounded.\r\n\r\nInstead of 39.52\u00a0 \u2248 40.0, do 39.52 \u2248 40\r\n\r\nInstead of 960.802 \u2248 961.000, do 960.802 \u2248 961\r\n\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound each of the following to the nearest whole number. Use the \u201capproximate equality\u201d sign <strong>\u2248<\/strong>.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>11.3\u00a0 \u2248\u00a0 11<\/li>\r\n \t<li>2.679<\/li>\r\n \t<li>403.8<\/li>\r\n \t<li>7.6<\/li>\r\n \t<li>65.91<\/li>\r\n \t<li>22.2<\/li>\r\n \t<li>3.76<\/li>\r\n \t<li>9.2<\/li>\r\n \t<li>1.7<\/li>\r\n \t<li>0.6<\/li>\r\n \t<li>2.63<\/li>\r\n \t<li>5.09<\/li>\r\n \t<li>19.8<\/li>\r\n \t<li>2.1<\/li>\r\n \t<li>0.7<\/li>\r\n \t<li>74.2<\/li>\r\n \t<li>3.61<\/li>\r\n \t<li>12.3<\/li>\r\n \t<li>34.5<\/li>\r\n \t<li>17.82<\/li>\r\n \t<li>2.45<\/li>\r\n \t<li>1.792<\/li>\r\n \t<li>2.01<\/li>\r\n \t<li>5.55<\/li>\r\n \t<li>10.3<\/li>\r\n \t<li>9.9<\/li>\r\n \t<li>8.15<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>11<\/li>\r\n \t<li>3<\/li>\r\n \t<li>404<\/li>\r\n \t<li>8<\/li>\r\n \t<li>66<\/li>\r\n \t<li>22<\/li>\r\n \t<li>4<\/li>\r\n \t<li>9<\/li>\r\n \t<li>2<\/li>\r\n \t<li>1<\/li>\r\n \t<li>3<\/li>\r\n \t<li>5<\/li>\r\n \t<li>20<\/li>\r\n \t<li>2<\/li>\r\n \t<li>1<\/li>\r\n \t<li>74<\/li>\r\n \t<li>4<\/li>\r\n \t<li>12<\/li>\r\n \t<li>35<\/li>\r\n \t<li>18<\/li>\r\n \t<li>2<\/li>\r\n \t<li>2<\/li>\r\n \t<li>2<\/li>\r\n \t<li>6<\/li>\r\n \t<li>10<\/li>\r\n \t<li>10<\/li>\r\n \t<li>8<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">\r\n\r\n<strong>Important Information<\/strong>\r\n\r\nIf these exercises on rounding are becoming tiresome, please do not despair\u2014there is a purpose. When you do operations (+ \u2212 \u00d7 \u00f7) with decimals, you will often end up with answers in the ten-thousandths place when you really only need the accuracy of a tenth or a hundredth place decimal. If you do decimal operations on a calculator, you may end up with 6 decimal places (millionths)\u2014not too practical if you are working with money and only want two decimal places! You will know how to round the answer to the decimal place you need for that question or situation.\r\n\r\n<\/div>\r\n<h1>Rounding Decimals to the Nearest Tenth<\/h1>\r\n<ul>\r\n \t<li>Underline the tenths place digit.<\/li>\r\n \t<li>Look at the digit (to the right) in the hundredths place. You can put an arrow above it to help you find it later.\r\n<ul>\r\n \t<li>If the hundredths digit is <strong>less than 5<\/strong>, the tenths digit does not change and the hundredths digit (and all other decimals numbers after the hundredths) are not written at all.<\/li>\r\n \t<li>If the hundredths digit is <strong>5 or more<\/strong>, increase the tenths digit by one and write no more decimals in the hundredths spot or after.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example G<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound to the nearest tenth.\r\n<ul type=\"none\">\r\n \t<li>[latex]\\begin{array}{l}\\hspace{6.2em}\\downarrow\\\\13.432\\rightarrow13.\\underline{4}32\\approx13.4\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{l}\\hspace{6.2em}\\downarrow\\\\13.476\\rightarrow13.\\underline{4}76\\approx13.5\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{l}\\hspace{5.1em}\\downarrow\\\\0.263\\rightarrow0.\\underline{2}63\\approx0.3\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{l}\\hspace{7.6em}\\downarrow\\\\234.0399\\rightarrow234.\\underline{0}399\\approx234.0\\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">Keep the 0 because you have accurately rounded off to that zero. It is called a significant figure.<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound each of the following to the nearest tenth.\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>4.23 \u2248 4.2<\/li>\r\n \t<li>5.18<\/li>\r\n \t<li>8.54<\/li>\r\n \t<li>16.09<\/li>\r\n \t<li>3.52<\/li>\r\n \t<li>4.14<span aria-label=\"blank\"> \u00a0<\/span><\/li>\r\n \t<li>6.24<\/li>\r\n \t<li>1.76<\/li>\r\n \t<li>1.74<\/li>\r\n \t<li>7.19<\/li>\r\n \t<li>2.15<\/li>\r\n \t<li>1.44<\/li>\r\n \t<li>3.172<\/li>\r\n \t<li>9.99<\/li>\r\n \t<li>5.09<\/li>\r\n \t<li>4.111<\/li>\r\n \t<li>6.046<\/li>\r\n \t<li>0.71<\/li>\r\n \t<li>3.63<\/li>\r\n \t<li>9.45<\/li>\r\n \t<li>12.36<\/li>\r\n \t<li>202.305<\/li>\r\n \t<li>2.66<\/li>\r\n \t<li>9.492<\/li>\r\n \t<li>7.388<\/li>\r\n \t<li>5.249<\/li>\r\n \t<li>2.45<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>4.2<\/li>\r\n \t<li>5.2<\/li>\r\n \t<li>8.5<\/li>\r\n \t<li>16.1<\/li>\r\n \t<li>3.5<\/li>\r\n \t<li>4.1<\/li>\r\n \t<li>6.2<\/li>\r\n \t<li>1.8<\/li>\r\n \t<li>1.7<\/li>\r\n \t<li>7.2<\/li>\r\n \t<li>2.2<\/li>\r\n \t<li>1.4<\/li>\r\n \t<li>3.2<\/li>\r\n \t<li>10.0<\/li>\r\n \t<li>5.1<\/li>\r\n \t<li>4.1<\/li>\r\n \t<li>6.0<\/li>\r\n \t<li>0.7<\/li>\r\n \t<li>3.6<\/li>\r\n \t<li>9.5<\/li>\r\n \t<li>12.4<\/li>\r\n \t<li>202.3<\/li>\r\n \t<li>2.7<\/li>\r\n \t<li>9.5<\/li>\r\n \t<li>7.4<\/li>\r\n \t<li>5.2<\/li>\r\n \t<li>2.5<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Rounding Decimals to the Nearest Hundredth<\/h1>\r\nRounding decimals to the nearest hundredth is similar to rounding to the nearest tenth.\r\n<ul>\r\n \t<li>Underline the hundredths place digit.<\/li>\r\n \t<li>Look at the digit (to the right) in the thousandths place. You can put an arrow above it to help you find it later.\r\n<ul>\r\n \t<li>If the thousandths digit is <strong>less than 5<\/strong>, the hundredths digit does not change and the thousandths digit (and all other decimals numbers after the hundredths) are not written at all.<\/li>\r\n \t<li>If the thousandths digit is <strong>5 or more<\/strong>, increase the hundredths digit by one and write no more decimals in the thousandths spot or after.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example H<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound to the nearest hundredth.\r\n\r\n[latex]\\begin{array}{l}\\hspace{7.1em}\\downarrow\\\\35.4524\\rightarrow35.4\\underline{5}24\\approx35.45\\end{array}[\/latex]\r\n\r\n[latex]\\begin{array}{l}\\hspace{7.1em}\\downarrow\\\\35.4567\\rightarrow35.4\\underline{5}67\\approx35.46\\end{array}[\/latex]\r\n\r\n[latex]\\begin{array}{l}\\hspace{7.1em}\\downarrow\\\\47.9873\\rightarrow47.9\\underline{8}73\\approx47.99\\end{array}[\/latex]\r\n\r\n[latex]\\begin{array}{l}\\hspace{7.6em}\\downarrow\\\\23.99609\\rightarrow23.9\\underline{9}609\\approx24.00\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">Keep these zeros because you have accurately rounded off to them.\r\nThese zeros are significant.<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound to the nearest hundredth. Keep significant zeros!\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>128.409 \u2248 128.41<\/li>\r\n \t<li>0.909<\/li>\r\n \t<li>98.024<\/li>\r\n \t<li>3.001<\/li>\r\n \t<li>76.3333<\/li>\r\n \t<li>0.229<\/li>\r\n \t<li>100.999<\/li>\r\n \t<li>0.756<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 6<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>128.41<\/li>\r\n \t<li>0.91<\/li>\r\n \t<li>98.02<\/li>\r\n \t<li>3.00<\/li>\r\n \t<li>76.33<\/li>\r\n \t<li>0.23<\/li>\r\n \t<li>101.00<\/li>\r\n \t<li>0.76<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h2>More Dollars and Cents<\/h2>\r\nA cent is what fraction of a dollar?\r\n\r\nYes, a cent is [latex]\\tfrac{1}{100}[\/latex] of a dollar (one hundredth).\r\n\r\nYou may be asked to round amounts of money to the nearest cent. What you are actually doing is rounding to the nearest hundredth of a dollar.\r\n<ul type=\"none\">\r\n \t<li>[latex]\\begin{array}{l}\\hspace{2.3em}\\downarrow\\\\\\$3.2\\underline{8}6\\approx\\$3.29\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{l}\\hspace{2.7em}\\downarrow\\\\\\$14.9\\underline{2}3\\approx\\$14.92\\end{array}[\/latex]<\/li>\r\n<\/ul>\r\none cent = one hundredth of a dollar\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound to the nearest cent.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>$42.008 \u2248 $42.01<\/li>\r\n \t<li>$ 0.233 \u2248 $0.23<\/li>\r\n \t<li>$25.255<\/li>\r\n \t<li>$10.141<\/li>\r\n \t<li>$0.706<\/li>\r\n \t<li>$100.999<\/li>\r\n \t<li>$0.9834<\/li>\r\n \t<li>$2.8977<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 7<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>$42.01<\/li>\r\n \t<li>$0.23<\/li>\r\n \t<li>$25.26<\/li>\r\n \t<li>$10.14<\/li>\r\n \t<li>$0.71<\/li>\r\n \t<li>$101.00<\/li>\r\n \t<li>$0.98<\/li>\r\n \t<li>$2.90<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Rounding Decimals to the Nearest Thousandth<\/h1>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example\u00a0 I<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound to the nearest thousandth (1000th).\r\n\r\n2.0486 \u21d2 2.0486\u00a0 \u2248\u00a0 \u00a02.049\r\n\r\nRound to the nearest thousandth (1000th).\r\n\r\n29.4324 \u21d2 29.4324 \u2248 29.432\r\n\r\n<\/div>\r\n<\/div>\r\nUse rounded numbers to estimate answers in daily situations, in math problem solving, and to get an idea of the answer before you figure something out on a calculator. Numbers that are rounded off make calculations simpler.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound the following numbers as called for at the left of the chart.\r\n<ol class=\"twocolumn\">\r\n \t<li>Round to the nearest tenth.\r\n<ol type=\"a\">\r\n \t<li>2.34 \u2248 2.3<\/li>\r\n \t<li>3.75<\/li>\r\n \t<li>1.028<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest thousandth.\r\n<ol type=\"a\">\r\n \t<li>0.1234<\/li>\r\n \t<li>1.8032<\/li>\r\n \t<li>7.0052<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest whole number.\r\n<ol type=\"a\">\r\n \t<li>21.1<\/li>\r\n \t<li>2.7<\/li>\r\n \t<li>12.05<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest hundred.\r\n<ol type=\"a\">\r\n \t<li>275<\/li>\r\n \t<li>490<\/li>\r\n \t<li>1260<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest hundredth.\r\n<ol type=\"a\">\r\n \t<li>1.732<\/li>\r\n \t<li>2.466<\/li>\r\n \t<li>3.074<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest ten.\r\n<ol type=\"a\">\r\n \t<li>68<\/li>\r\n \t<li>32<\/li>\r\n \t<li>824<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest thousandth.\r\n<ol type=\"a\">\r\n \t<li>0.7286<\/li>\r\n \t<li>0.5027<\/li>\r\n \t<li>1.2345<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 8<\/strong>\r\n<ol class=\"twocolumn\">\r\n \t<li>Round to the nearest tenth.\r\n<ol type=\"a\">\r\n \t<li>2.3<\/li>\r\n \t<li>3.8<\/li>\r\n \t<li>1.0<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest thousandth.\r\n<ol type=\"a\">\r\n \t<li>0.123<\/li>\r\n \t<li>1.803<\/li>\r\n \t<li>7.005<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest whole number.\r\n<ol type=\"a\">\r\n \t<li>21<\/li>\r\n \t<li>3<\/li>\r\n \t<li>12<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest hundred.\r\n<ol type=\"a\">\r\n \t<li>300<\/li>\r\n \t<li>500<\/li>\r\n \t<li>1300<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest hundredth.\r\n<ol type=\"a\">\r\n \t<li>1.73<\/li>\r\n \t<li>2.47<\/li>\r\n \t<li>3.07<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest ten.\r\n<ol type=\"a\">\r\n \t<li>70<\/li>\r\n \t<li>30<\/li>\r\n \t<li>820<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest thousandth.\r\n<ol type=\"a\">\r\n \t<li>0.729<\/li>\r\n \t<li>0.503<\/li>\r\n \t<li>1.235<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRound the numbers to estimate the answer. Circle the estimate that is the best answer.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>47 \u00d7 52 \u2248 240, <span style=\"border: 1px solid;border-radius: 30px;padding: 2px 2px 2px 2px\"> 2<span style=\"margin-left: 0.25em\">500<\/span> <\/span>, 250, 2<span style=\"margin-left: 0.25em\">600<\/span>\r\nEstimation: 50 \u00d7 50 = 2<span style=\"margin-left: 0.25em\">500<\/span><\/li>\r\n \t<li>3.2 \u00d7 4.875 \u2248 6, 8, 15, 17<\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">149<\/span> \u00f7 20 \u2248 2<span style=\"margin-left: 0.25em\">000<\/span>, 200, 20, 230<\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">895<\/span> + 2<span style=\"margin-left: 0.25em\">895<\/span> \u2248 600, 6<span style=\"margin-left: 0.25em\">000<\/span>, 4<span style=\"margin-left: 0.25em\">000<\/span>, 5<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>91 \u00d7 79 \u2248 720, 800, 8<span style=\"margin-left: 0.25em\">000<\/span>, 80<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>347 \u00f7 50 \u2248 7, 70, 700, 8<\/li>\r\n \t<li>4<span style=\"margin-left: 0.25em\">892<\/span> \u2212 3<span style=\"margin-left: 0.25em\">012<\/span> \u2248 1<span style=\"margin-left: 0.25em\">500<\/span>, 1<span style=\"margin-left: 0.25em\">000<\/span>, 2<span style=\"margin-left: 0.25em\">000<\/span>, 2<span style=\"margin-left: 0.25em\">500<\/span><\/li>\r\n \t<li>Nathan drives to Terrace and back once a week. He averages 286 km per week. Estimate how many kilometres he drives in one year (52 weeks).<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 9<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>2<span style=\"margin-left: 0.25em\">500<\/span><\/li>\r\n \t<li>15<\/li>\r\n \t<li>200<\/li>\r\n \t<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>8<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>7<\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\r\n \t<li>15<span style=\"margin-left: 0.25em\">000<\/span> km<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Topic D: Self-Test<\/h1>\r\n<strong>Mark \/10\u00a0 \u00a0 \u00a0Aim 8\/10<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Round to the nearest hundred. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>749<\/li>\r\n \t<li>691<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest whole number. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>0.831<\/li>\r\n \t<li>6.24<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest tenth. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>8.29<\/li>\r\n \t<li>6.533<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest hundredth. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>34.792<\/li>\r\n \t<li>6.459<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest thousandth. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>5.4392<\/li>\r\n \t<li>0.8208<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Estimate the answer. (2 marks)\r\n<ol type=\"a\">\r\n \t<li>Mary baby-sat for her twin nephews for 6.75 hours on Saturday. She is paid $8.40 an hour. Estimate her earnings by rounding the numbers in the problem to whole numbers. Show how you worked out the estimate.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic D Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>Round to the nearest hundred. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>700<\/li>\r\n \t<li>700<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest whole number. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>1<\/li>\r\n \t<li>6<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest tenth. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>8.3<\/li>\r\n \t<li>6.5<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest hundredth. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>34.79<\/li>\r\n \t<li>6.46<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Round to the nearest thousandth. (2 marks)\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>5.439<\/li>\r\n \t<li>0.821<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Estimate the answer. (2 marks)\r\n<ol type=\"a\">\r\n \t<li>Estimation: 7 hours \u00d7 $8 \u2248 $56<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>If a pair of jeans cost $49.98, what amount would you say if someone asks what you paid for them? You would probably say, &#8220;They cost around $50.&#8221;<\/p>\n<p>We often round cents to dollars as we go about our lives. You may already have an idea of how to do this. For example, answer these questions.<\/p>\n<ul>\n<li>About how much do your groceries cost each month?<\/li>\n<li>About how much does it cost to fill a small car&#8217;s gas tank?<\/li>\n<\/ul>\n<p>Look at your answers. The amount for groceries may be quite large. When you estimated your answer, how did you round the amount? For example, if your real monthly grocery bill was $481.73 you might have said $482 or perhaps $480.\u00a0 Perhaps you even have estimated to the nearest hundred dollars and said, &#8220;About $500 a month for groceries.&#8221; All those estimates would be correct.<\/p>\n<div class=\"textbox\">\n<p>The amount for a tank of gas is less than a month&#8217;s groceries. How did you estimate?<\/p>\n<p>For example, a small car may take $54.72 of gas.<\/p>\n<p class=\"indent\">If you estimated to the nearest dollar, you would say, &#8220;About $55.&#8221;<\/p>\n<p class=\"indent\">If you estimated to the nearest ten dollars, you would say, &#8220;About $50.&#8221;<\/p>\n<p class=\"indent\">If you rounded to the nearest dollar you would say, &#8220;54 dollars.&#8221;<\/p>\n<\/div>\n<p>We round a number in different ways depending on several things:<\/p>\n<ul>\n<li>the size of the number we are rounding<\/li>\n<li>what we are going to do with the number after we have rounded it off<\/li>\n<li>our own convenience<\/li>\n<\/ul>\n<p>Carefully review the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_55_200\">place value<\/a> for whole numbers.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<th style=\"text-align: center\" colspan=\"3\" scope=\"col\">Thousands<\/th>\n<th class=\"shaded\" style=\"text-align: center\" colspan=\"3\" scope=\"col\">Ones<\/th>\n<th scope=\"col\"><\/th>\n<\/tr>\n<tr>\n<td style=\"width: 14%;text-align: center\" scope=\"col\">Hundred thousands<\/td>\n<td style=\"width: 14%;text-align: center\" scope=\"col\">Ten thousands<\/td>\n<td style=\"width: 14%;text-align: center\" scope=\"col\">One thousand<\/td>\n<td class=\"shaded\" style=\"width: 14%;text-align: center\" scope=\"col\">Hundreds<\/td>\n<td class=\"shaded\" style=\"width: 14%;text-align: center\" scope=\"col\">Tens<\/td>\n<td class=\"shaded\" style=\"width: 14%;text-align: center\" scope=\"col\">Ones<\/td>\n<td style=\"width: 14%;text-align: center\" scope=\"col\">Decimal<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Rounding Whole Numbers<\/h1>\n<p>We round <strong>down<\/strong> if the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_55_169\">digit<\/a> to the right is less than 5. We round <strong>up<\/strong> if the digit to the right is 5 or more.<\/p>\n<ul>\n<li>Rounding numbers gives an approximate amount; it is not an accurate figure.<\/li>\n<li>Use a different form of the equal sign (\u2248) which means \u201capproximate equality.\u201d<\/li>\n<\/ul>\n<h2>Review: Rounding to the Nearest Ten<\/h2>\n<ul>\n<li>Underline the tens digit<\/li>\n<li>Look at the digit in the ones place (to the right). You can put an arrow above it to help you find it later.\n<ul>\n<li>If the ones digit is <strong>5 or more, round up<\/strong>. Write the ones digit as zero and increase the tens digit by one.<\/li>\n<li>If the ones digit is <strong>less than 5, round down<\/strong>. The tens digit does not change and the ones digit is written as a zero.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>\u00a0[latex]\\begin{array}{r}\\downarrow\\\\\\underline{2}3\\end{array}[\/latex]<\/p>\n<p>23 is rounded down to 20. The tens digit stays the same.<\/p>\n<p>23 \u2248 20<\/p>\n<\/div>\n<\/div>\n<p>Here&#8217;s another example:<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}{r}\\downarrow\\\\2\\underline{8}7\\end{array}[\/latex]<\/p>\n<p>287 is rounded up to 290. The tens digit increases by 1.<\/p>\n<p>287 \u2248 290.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round each of the following to the nearest ten. Use the \u201capproximate equality\u201d sign \u2248.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>46 \u2248 50<\/li>\n<li>111 \u2248 110<\/li>\n<li>7 \u2248<\/li>\n<li>116 \u2248<\/li>\n<li>71 \u2248<\/li>\n<li>89 \u2248<\/li>\n<li>96 \u2248<\/li>\n<li>4 \u2248<\/li>\n<li>385 \u2248<\/li>\n<li>108 \u2248<\/li>\n<li>73 \u2248<\/li>\n<li>17 \u2248<\/li>\n<li>361 \u2248<\/li>\n<li>8 \u2248<\/li>\n<li>49 \u2248<\/li>\n<li>148 \u2248<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>50<\/li>\n<li>110<\/li>\n<li>10<\/li>\n<li>120<\/li>\n<li>70<\/li>\n<li>90<\/li>\n<li>100<\/li>\n<li>0<\/li>\n<li>390<\/li>\n<li>110<\/li>\n<li>70<\/li>\n<li>20<\/li>\n<li>360<\/li>\n<li>10<\/li>\n<li>50<\/li>\n<li>150<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h2>Review: Rounding to the Nearest Hundred<\/h2>\n<ul>\n<li>Underline the hundreds digit.<\/li>\n<li>Look at the digit in the tens place (to the right). You can put an arrow above it to help you find it later.\n<ul>\n<li>If the tens digit is <strong>5 or more, round up<\/strong>. Write the tens and ones digit as zero and increase the hundreds digit by one.<\/li>\n<li>If the tens digit is <strong>less than 5, round down<\/strong>. The hundreds digit does not change and the tens and ones digit is written as a zero.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>\u00a0[latex]\\begin{array}{c}\\downarrow\\\\ \\underline{4}73\\end{array}[\/latex]<\/p>\n<p>473 is rounded up to 500.<\/p>\n<p>473 \u2248 500<\/p>\n<\/div>\n<\/div>\n<p>Round down if the tens digit is less than 5 and up if it is 5 or more:<\/p>\n<ul>\n<li>728 rounded to the nearest hundred is 700. (The tens digit is 2, which is less than 5, so the hundreds digit stays the same.)<\/li>\n<li>758 rounded to the nearest hundred is 800. (The tens digit is 5, which is five or more, so the hundreds digit increases by 1.)<\/li>\n<\/ul>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round each of the following to the nearest HUNDRED. Use the \u201capproximate equality\u201d sign \u2248.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>330\u00a0 \u2248\u00a0 300<\/li>\n<li>908<\/li>\n<li>2795<\/li>\n<li>1260<\/li>\n<li>742<\/li>\n<li>127<\/li>\n<li>302<\/li>\n<li>945<\/li>\n<li>865<\/li>\n<li>275<\/li>\n<li>590<\/li>\n<li>1240<\/li>\n<li>214<\/li>\n<li>4450<\/li>\n<li>98<\/li>\n<li>996<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>300<\/li>\n<li>900<\/li>\n<li>2<span style=\"margin-left: 0.25em\">800<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">300<\/span><\/li>\n<li>700<\/li>\n<li>100<\/li>\n<li>300<\/li>\n<li>900<\/li>\n<li>900<\/li>\n<li>300<\/li>\n<li>600<\/li>\n<li>1<span style=\"margin-left: 0.25em\">200<\/span><\/li>\n<li>200<\/li>\n<li>4<span style=\"margin-left: 0.25em\">500<\/span><\/li>\n<li><span style=\"margin-left: 0.25em\">100<\/span><\/li>\n<li><span style=\"margin-left: 0.25em\">1<span style=\"margin-left: 0.25em\">000<\/span><\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h2>Review: Rounding to the Nearest Thousand<\/h2>\n<ul>\n<li>Underline the thousands digit<\/li>\n<li>Look at the digit in the hundreds place (to the right). You can put an arrow above it to help you find it later.\n<ul>\n<li>If the hundreds digit is <strong>5 or more, round up<\/strong>. Write the hundreds, tens and ones digit as zero and increase the thousands digit by one.<\/li>\n<li>If the hundreds digit is <strong>less than 5, round down<\/strong>. The thousands digit does not change and the hundreds, tens and ones digit is written as a zero.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example D<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}{l}\\hspace{0.5em}\\downarrow\\\\ \\underline{3}485\\end{array}[\/latex]<\/p>\n<p>3<span style=\"margin-left: 0.25em\">485<\/span> is rounded down to 3<span style=\"margin-left: 0.25em\">000<\/span>.<\/p>\n<p>3<span style=\"margin-left: 0.25em\">485<\/span> \u2248 3<span style=\"margin-left: 0.25em\">000<\/span><\/p>\n<\/div>\n<\/div>\n<p>Round down if the hundreds digit is less than 5 and round up if it is 5 or more:<\/p>\n<ul>\n<li>2<span style=\"margin-left: 0.25em\">109<\/span> rounded to the nearest thousand is 2<span style=\"margin-left: 0.25em\">000<\/span>. (The hundreds digit is 1, which is less than 5.)<\/li>\n<li>2<span style=\"margin-left: 0.25em\">643<\/span> rounded to the nearest thousand is 3<span style=\"margin-left: 0.25em\">000<\/span>. (The hundreds digit is 6, which is more than 5.)<\/li>\n<li>0940 rounded to the nearest thousand is 1<span style=\"margin-left: 0.25em\">000<\/span>. (The hundreds digit is 9, which is more than 5, so the thousands digit increases from 0 to 1.)<\/li>\n<li>0465 rounded to the nearest thousand is 0. (The hundreds digit is 4, which is less than 5, so the thousands digit stays at 0.)<\/li>\n<\/ul>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round each of the following to the nearest thousand. Use the \u201capproximate equality\u201d sign \u2248.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>1<span style=\"margin-left: 0.25em\">760<\/span>\u00a0 \u2248\u00a0 2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">250<\/span><\/li>\n<li>850\u00a0<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/li>\n<li>320<\/li>\n<li>5<span style=\"margin-left: 0.25em\">544<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">234\u00a0<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span><\/li>\n<li>492<\/li>\n<li>6<span style=\"margin-left: 0.25em\">199<\/span><\/li>\n<li>9<span style=\"margin-left: 0.25em\">883<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">045<\/span><\/li>\n<li>7<span style=\"margin-left: 0.25em\">856<\/span><\/li>\n<li>500<\/li>\n<li>1<span style=\"margin-left: 0.25em\">780<\/span><\/li>\n<li>495<\/li>\n<li>9<span style=\"margin-left: 0.25em\">300<\/span><\/li>\n<li>700<\/li>\n<li>2<span style=\"margin-left: 0.25em\">449<\/span><\/li>\n<li>5<span style=\"margin-left: 0.25em\">555<\/span><\/li>\n<li>8<span style=\"margin-left: 0.25em\">914<\/span><\/li>\n<li>85<span style=\"margin-left: 0.25em\">455<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">475\u00a0<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span><\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>0<\/li>\n<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li><span style=\"margin-left: 0.25em\">0<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>10<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>8<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>0<\/li>\n<li>9<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>1<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>9<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>85<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Rounding Decimals to Whole Numbers<\/h1>\n<p>Remember, decimals are part of the whole thing. We can round the decimal to the nearest whole number. Rounding to whole numbers means rounding off to the ones place.<\/p>\n<p>When rounding to the whole number:<\/p>\n<ul>\n<li>Underline the ones digit<\/li>\n<li>Look at the digit in the thenths place (to the right). You can put an arrow above it to help you find it later.\n<ul>\n<li>If the tenths digit is <strong>5 or more, round up<\/strong>. Increase the ones digit by one. Do not write a decimal or any decimal digits.<\/li>\n<li>If the tenths digit is <strong>less than 5, round down<\/strong>. The ones digit does not change. Do not write a decimal or any decimal digits,<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example E<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\begin{array}{l}\\hspace{1.3em}\\downarrow\\\\ 3\\underline{7}.482\\end{array}[\/latex]<\/p>\n<p>37.482 rounded to the nearest whole number is 37. (The tenths digit is 4, which is less than 5.)<\/p>\n<p>37.482 \u2248 37<\/p>\n<p>[latex]\\begin{array}{l}\\hspace{1.3em}\\downarrow\\\\ 3\\underline{7}.906\\end{array}[\/latex]<\/p>\n<p>37.906\u00a0 rounded to the nearest whole number is 38. (The tenths digit is 9, which is more than 5.)<\/p>\n<p>37. 906 \u2248 38<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example F<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>Round to a whole number.<br \/>\n[latex]\\begin{array}{l}\\hspace{5.58em}\\downarrow\\\\ 42.123\\rightarrow4\\underline{2}.123\\approx42\\end{array}[\/latex]<\/li>\n<li>Round 960.802 to the nearest whole number.<br \/>\n[latex]\\begin{array}{l}\\hspace{6.6em}\\downarrow\\\\ 960.802\\rightarrow96\\underline{0}.802\\approx961\\end{array}[\/latex]<\/li>\n<li>Round 39.5 to the nearest ones.<br \/>\n[latex]\\begin{array}{l}\\hspace{4.6em}\\downarrow\\\\ 39.5\\rightarrow3\\underline{9}.5\\approx40\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<p><strong>Z<\/strong><strong>e<\/strong><strong>r<\/strong><strong>os again \u2013 <\/strong><\/p>\n<p>You know that zeros at the end of a decimal do not change the value of the amount. You can add as many as you like.<\/p>\n<p>But when a decimal has been rounded, drop any zeros after the place where you have rounded.<\/p>\n<p>Instead of 39.52\u00a0 \u2248 40.0, do 39.52 \u2248 40<\/p>\n<p>Instead of 960.802 \u2248 961.000, do 960.802 \u2248 961<\/p>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round each of the following to the nearest whole number. Use the \u201capproximate equality\u201d sign <strong>\u2248<\/strong>.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>11.3\u00a0 \u2248\u00a0 11<\/li>\n<li>2.679<\/li>\n<li>403.8<\/li>\n<li>7.6<\/li>\n<li>65.91<\/li>\n<li>22.2<\/li>\n<li>3.76<\/li>\n<li>9.2<\/li>\n<li>1.7<\/li>\n<li>0.6<\/li>\n<li>2.63<\/li>\n<li>5.09<\/li>\n<li>19.8<\/li>\n<li>2.1<\/li>\n<li>0.7<\/li>\n<li>74.2<\/li>\n<li>3.61<\/li>\n<li>12.3<\/li>\n<li>34.5<\/li>\n<li>17.82<\/li>\n<li>2.45<\/li>\n<li>1.792<\/li>\n<li>2.01<\/li>\n<li>5.55<\/li>\n<li>10.3<\/li>\n<li>9.9<\/li>\n<li>8.15<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>11<\/li>\n<li>3<\/li>\n<li>404<\/li>\n<li>8<\/li>\n<li>66<\/li>\n<li>22<\/li>\n<li>4<\/li>\n<li>9<\/li>\n<li>2<\/li>\n<li>1<\/li>\n<li>3<\/li>\n<li>5<\/li>\n<li>20<\/li>\n<li>2<\/li>\n<li>1<\/li>\n<li>74<\/li>\n<li>4<\/li>\n<li>12<\/li>\n<li>35<\/li>\n<li>18<\/li>\n<li>2<\/li>\n<li>2<\/li>\n<li>2<\/li>\n<li>6<\/li>\n<li>10<\/li>\n<li>10<\/li>\n<li>8<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<p><strong>Important Information<\/strong><\/p>\n<p>If these exercises on rounding are becoming tiresome, please do not despair\u2014there is a purpose. When you do operations (+ \u2212 \u00d7 \u00f7) with decimals, you will often end up with answers in the ten-thousandths place when you really only need the accuracy of a tenth or a hundredth place decimal. If you do decimal operations on a calculator, you may end up with 6 decimal places (millionths)\u2014not too practical if you are working with money and only want two decimal places! You will know how to round the answer to the decimal place you need for that question or situation.<\/p>\n<\/div>\n<h1>Rounding Decimals to the Nearest Tenth<\/h1>\n<ul>\n<li>Underline the tenths place digit.<\/li>\n<li>Look at the digit (to the right) in the hundredths place. You can put an arrow above it to help you find it later.\n<ul>\n<li>If the hundredths digit is <strong>less than 5<\/strong>, the tenths digit does not change and the hundredths digit (and all other decimals numbers after the hundredths) are not written at all.<\/li>\n<li>If the hundredths digit is <strong>5 or more<\/strong>, increase the tenths digit by one and write no more decimals in the hundredths spot or after.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example G<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round to the nearest tenth.<\/p>\n<ul type=\"none\">\n<li>[latex]\\begin{array}{l}\\hspace{6.2em}\\downarrow\\\\13.432\\rightarrow13.\\underline{4}32\\approx13.4\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{l}\\hspace{6.2em}\\downarrow\\\\13.476\\rightarrow13.\\underline{4}76\\approx13.5\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{l}\\hspace{5.1em}\\downarrow\\\\0.263\\rightarrow0.\\underline{2}63\\approx0.3\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{l}\\hspace{7.6em}\\downarrow\\\\234.0399\\rightarrow234.\\underline{0}399\\approx234.0\\end{array}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox\">Keep the 0 because you have accurately rounded off to that zero. It is called a significant figure.<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round each of the following to the nearest tenth.<\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>4.23 \u2248 4.2<\/li>\n<li>5.18<\/li>\n<li>8.54<\/li>\n<li>16.09<\/li>\n<li>3.52<\/li>\n<li>4.14<span aria-label=\"blank\"> \u00a0<\/span><\/li>\n<li>6.24<\/li>\n<li>1.76<\/li>\n<li>1.74<\/li>\n<li>7.19<\/li>\n<li>2.15<\/li>\n<li>1.44<\/li>\n<li>3.172<\/li>\n<li>9.99<\/li>\n<li>5.09<\/li>\n<li>4.111<\/li>\n<li>6.046<\/li>\n<li>0.71<\/li>\n<li>3.63<\/li>\n<li>9.45<\/li>\n<li>12.36<\/li>\n<li>202.305<\/li>\n<li>2.66<\/li>\n<li>9.492<\/li>\n<li>7.388<\/li>\n<li>5.249<\/li>\n<li>2.45<span aria-label=\"blank\"> \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>4.2<\/li>\n<li>5.2<\/li>\n<li>8.5<\/li>\n<li>16.1<\/li>\n<li>3.5<\/li>\n<li>4.1<\/li>\n<li>6.2<\/li>\n<li>1.8<\/li>\n<li>1.7<\/li>\n<li>7.2<\/li>\n<li>2.2<\/li>\n<li>1.4<\/li>\n<li>3.2<\/li>\n<li>10.0<\/li>\n<li>5.1<\/li>\n<li>4.1<\/li>\n<li>6.0<\/li>\n<li>0.7<\/li>\n<li>3.6<\/li>\n<li>9.5<\/li>\n<li>12.4<\/li>\n<li>202.3<\/li>\n<li>2.7<\/li>\n<li>9.5<\/li>\n<li>7.4<\/li>\n<li>5.2<\/li>\n<li>2.5<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Rounding Decimals to the Nearest Hundredth<\/h1>\n<p>Rounding decimals to the nearest hundredth is similar to rounding to the nearest tenth.<\/p>\n<ul>\n<li>Underline the hundredths place digit.<\/li>\n<li>Look at the digit (to the right) in the thousandths place. You can put an arrow above it to help you find it later.\n<ul>\n<li>If the thousandths digit is <strong>less than 5<\/strong>, the hundredths digit does not change and the thousandths digit (and all other decimals numbers after the hundredths) are not written at all.<\/li>\n<li>If the thousandths digit is <strong>5 or more<\/strong>, increase the hundredths digit by one and write no more decimals in the thousandths spot or after.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example H<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round to the nearest hundredth.<\/p>\n<p>[latex]\\begin{array}{l}\\hspace{7.1em}\\downarrow\\\\35.4524\\rightarrow35.4\\underline{5}24\\approx35.45\\end{array}[\/latex]<\/p>\n<p>[latex]\\begin{array}{l}\\hspace{7.1em}\\downarrow\\\\35.4567\\rightarrow35.4\\underline{5}67\\approx35.46\\end{array}[\/latex]<\/p>\n<p>[latex]\\begin{array}{l}\\hspace{7.1em}\\downarrow\\\\47.9873\\rightarrow47.9\\underline{8}73\\approx47.99\\end{array}[\/latex]<\/p>\n<p>[latex]\\begin{array}{l}\\hspace{7.6em}\\downarrow\\\\23.99609\\rightarrow23.9\\underline{9}609\\approx24.00\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox\">Keep these zeros because you have accurately rounded off to them.<br \/>\nThese zeros are significant.<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round to the nearest hundredth. Keep significant zeros!<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>128.409 \u2248 128.41<\/li>\n<li>0.909<\/li>\n<li>98.024<\/li>\n<li>3.001<\/li>\n<li>76.3333<\/li>\n<li>0.229<\/li>\n<li>100.999<\/li>\n<li>0.756<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 6<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>128.41<\/li>\n<li>0.91<\/li>\n<li>98.02<\/li>\n<li>3.00<\/li>\n<li>76.33<\/li>\n<li>0.23<\/li>\n<li>101.00<\/li>\n<li>0.76<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h2>More Dollars and Cents<\/h2>\n<p>A cent is what fraction of a dollar?<\/p>\n<p>Yes, a cent is [latex]\\tfrac{1}{100}[\/latex] of a dollar (one hundredth).<\/p>\n<p>You may be asked to round amounts of money to the nearest cent. What you are actually doing is rounding to the nearest hundredth of a dollar.<\/p>\n<ul type=\"none\">\n<li>[latex]\\begin{array}{l}\\hspace{2.3em}\\downarrow\\\\\\$3.2\\underline{8}6\\approx\\$3.29\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{l}\\hspace{2.7em}\\downarrow\\\\\\$14.9\\underline{2}3\\approx\\$14.92\\end{array}[\/latex]<\/li>\n<\/ul>\n<p>one cent = one hundredth of a dollar<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round to the nearest cent.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>$42.008 \u2248 $42.01<\/li>\n<li>$ 0.233 \u2248 $0.23<\/li>\n<li>$25.255<\/li>\n<li>$10.141<\/li>\n<li>$0.706<\/li>\n<li>$100.999<\/li>\n<li>$0.9834<\/li>\n<li>$2.8977<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 7<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>$42.01<\/li>\n<li>$0.23<\/li>\n<li>$25.26<\/li>\n<li>$10.14<\/li>\n<li>$0.71<\/li>\n<li>$101.00<\/li>\n<li>$0.98<\/li>\n<li>$2.90<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Rounding Decimals to the Nearest Thousandth<\/h1>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example\u00a0 I<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round to the nearest thousandth (1000th).<\/p>\n<p>2.0486 \u21d2 2.0486\u00a0 \u2248\u00a0 \u00a02.049<\/p>\n<p>Round to the nearest thousandth (1000th).<\/p>\n<p>29.4324 \u21d2 29.4324 \u2248 29.432<\/p>\n<\/div>\n<\/div>\n<p>Use rounded numbers to estimate answers in daily situations, in math problem solving, and to get an idea of the answer before you figure something out on a calculator. Numbers that are rounded off make calculations simpler.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round the following numbers as called for at the left of the chart.<\/p>\n<ol class=\"twocolumn\">\n<li>Round to the nearest tenth.\n<ol type=\"a\">\n<li>2.34 \u2248 2.3<\/li>\n<li>3.75<\/li>\n<li>1.028<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest thousandth.\n<ol type=\"a\">\n<li>0.1234<\/li>\n<li>1.8032<\/li>\n<li>7.0052<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest whole number.\n<ol type=\"a\">\n<li>21.1<\/li>\n<li>2.7<\/li>\n<li>12.05<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest hundred.\n<ol type=\"a\">\n<li>275<\/li>\n<li>490<\/li>\n<li>1260<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest hundredth.\n<ol type=\"a\">\n<li>1.732<\/li>\n<li>2.466<\/li>\n<li>3.074<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest ten.\n<ol type=\"a\">\n<li>68<\/li>\n<li>32<\/li>\n<li>824<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest thousandth.\n<ol type=\"a\">\n<li>0.7286<\/li>\n<li>0.5027<\/li>\n<li>1.2345<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 8<\/strong><\/p>\n<ol class=\"twocolumn\">\n<li>Round to the nearest tenth.\n<ol type=\"a\">\n<li>2.3<\/li>\n<li>3.8<\/li>\n<li>1.0<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest thousandth.\n<ol type=\"a\">\n<li>0.123<\/li>\n<li>1.803<\/li>\n<li>7.005<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest whole number.\n<ol type=\"a\">\n<li>21<\/li>\n<li>3<\/li>\n<li>12<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest hundred.\n<ol type=\"a\">\n<li>300<\/li>\n<li>500<\/li>\n<li>1300<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest hundredth.\n<ol type=\"a\">\n<li>1.73<\/li>\n<li>2.47<\/li>\n<li>3.07<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest ten.\n<ol type=\"a\">\n<li>70<\/li>\n<li>30<\/li>\n<li>820<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest thousandth.\n<ol type=\"a\">\n<li>0.729<\/li>\n<li>0.503<\/li>\n<li>1.235<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Round the numbers to estimate the answer. Circle the estimate that is the best answer.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>47 \u00d7 52 \u2248 240, <span style=\"border: 1px solid;border-radius: 30px;padding: 2px 2px 2px 2px\"> 2<span style=\"margin-left: 0.25em\">500<\/span> <\/span>, 250, 2<span style=\"margin-left: 0.25em\">600<\/span><br \/>\nEstimation: 50 \u00d7 50 = 2<span style=\"margin-left: 0.25em\">500<\/span><\/li>\n<li>3.2 \u00d7 4.875 \u2248 6, 8, 15, 17<\/li>\n<li>4<span style=\"margin-left: 0.25em\">149<\/span> \u00f7 20 \u2248 2<span style=\"margin-left: 0.25em\">000<\/span>, 200, 20, 230<\/li>\n<li>2<span style=\"margin-left: 0.25em\">895<\/span> + 2<span style=\"margin-left: 0.25em\">895<\/span> \u2248 600, 6<span style=\"margin-left: 0.25em\">000<\/span>, 4<span style=\"margin-left: 0.25em\">000<\/span>, 5<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>91 \u00d7 79 \u2248 720, 800, 8<span style=\"margin-left: 0.25em\">000<\/span>, 80<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>347 \u00f7 50 \u2248 7, 70, 700, 8<\/li>\n<li>4<span style=\"margin-left: 0.25em\">892<\/span> \u2212 3<span style=\"margin-left: 0.25em\">012<\/span> \u2248 1<span style=\"margin-left: 0.25em\">500<\/span>, 1<span style=\"margin-left: 0.25em\">000<\/span>, 2<span style=\"margin-left: 0.25em\">000<\/span>, 2<span style=\"margin-left: 0.25em\">500<\/span><\/li>\n<li>Nathan drives to Terrace and back once a week. He averages 286 km per week. Estimate how many kilometres he drives in one year (52 weeks).<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 9<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>2<span style=\"margin-left: 0.25em\">500<\/span><\/li>\n<li>15<\/li>\n<li>200<\/li>\n<li>6<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>8<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>7<\/li>\n<li>2<span style=\"margin-left: 0.25em\">000<\/span><\/li>\n<li>15<span style=\"margin-left: 0.25em\">000<\/span> km<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Topic D: Self-Test<\/h1>\n<p><strong>Mark \/10\u00a0 \u00a0 \u00a0Aim 8\/10<\/strong><\/p>\n<ol type=\"A\">\n<li>Round to the nearest hundred. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>749<\/li>\n<li>691<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest whole number. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>0.831<\/li>\n<li>6.24<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest tenth. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>8.29<\/li>\n<li>6.533<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest hundredth. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>34.792<\/li>\n<li>6.459<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest thousandth. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>5.4392<\/li>\n<li>0.8208<\/li>\n<\/ol>\n<\/li>\n<li>Estimate the answer. (2 marks)\n<ol type=\"a\">\n<li>Mary baby-sat for her twin nephews for 6.75 hours on Saturday. She is paid $8.40 an hour. Estimate her earnings by rounding the numbers in the problem to whole numbers. Show how you worked out the estimate.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic D Self-Test<\/h2>\n<ol type=\"A\">\n<li>Round to the nearest hundred. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>700<\/li>\n<li>700<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest whole number. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>1<\/li>\n<li>6<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest tenth. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>8.3<\/li>\n<li>6.5<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest hundredth. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>34.79<\/li>\n<li>6.46<\/li>\n<\/ol>\n<\/li>\n<li>Round to the nearest thousandth. (2 marks)\n<ol class=\"twocolumn\" type=\"a\">\n<li>5.439<\/li>\n<li>0.821<\/li>\n<\/ol>\n<\/li>\n<li>Estimate the answer. (2 marks)\n<ol type=\"a\">\n<li>Estimation: 7 hours \u00d7 $8 \u2248 $56<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_55_200\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_55_200\"><div tabindex=\"-1\"><p>We understand numbers by the way the digits (numerals) are arranged in relationship to each other and to the decimal point. Each position has a certain value. Our number system is a <strong>decimal system<\/strong>. The place value is based on <strong>ten<\/strong>.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_55_169\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_55_169\"><div tabindex=\"-1\"><p>Any of the ten numerals (0 to 9) are digits. This term comes from our ten fingers which are called digits. The numerals came to be called \"digits\" from the practice of counting on the fingers!<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":999,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-55","chapter","type-chapter","status-publish","hentry"],"part":24,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/55","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":5,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/55\/revisions"}],"predecessor-version":[{"id":258,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/55\/revisions\/258"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/parts\/24"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapters\/55\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/media?parent=55"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/pressbooks\/v2\/chapter-type?post=55"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/contributor?post=55"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math024\/wp-json\/wp\/v2\/license?post=55"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}