{"id":182,"date":"2023-07-30T13:47:06","date_gmt":"2023-07-30T17:47:06","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/?post_type=chapter&#038;p=182"},"modified":"2023-11-03T12:24:49","modified_gmt":"2023-11-03T16:24:49","slug":"power-of-ten","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/chapter\/power-of-ten\/","title":{"raw":"Understanding the Rule for Powers of Ten","rendered":"Understanding the Rule for Powers of Ten"},"content":{"raw":"Raising 10 to a power means multiplying 10 by itself a certain number of times. The number of times you multiply 10 is equal to the exponent. So, for example, 10 to the power of 3 means multiplying 10 by itself 3 times, resulting in the number 1000.\r\n\r\nThis looks like 10<sup>3<\/sup> = 10 \u00d7 10 \u00d7 10 = 1000\r\n<h2>Electrical Units<\/h2>\r\nElectricians use quantities in very large numbers or very small numbers.\r\n<ul>\r\n \t<li>Large Unit Example: Transmission lines transmit at voltages of 500,000 volts.<\/li>\r\n \t<li>Small Unit Example: Computers deal in currents of 0.000 000 001 amperes.<\/li>\r\n<\/ul>\r\nIt is very easy to miss a zero when writing the numbers out!\r\n\r\nThe solution is to express all of the numbers in terms of POWER OF 10.\r\n\r\nEngineering notation uses only those powers of 10 with an exponent that is a multiple of three.\r\n\r\nExample: 10<sup>-9<\/sup> , 10<sup>-6<\/sup> , 10<sup>-3<\/sup> , 10<sup>3<\/sup> , 10<sup>6<\/sup>\r\n\r\nEach one of these engineering metric notational values is associated with a prefix. Instead of writing a number with a large power of 10, a metric prefix which represents the multiplier is placed ahead of the UNIT.\r\n\r\nExample:\r\n\r\n25 000 Volts = 25 \u00d7 103 Volts = 25 Kilovolts = <strong>25 kV<\/strong> (the kilo represents 103)\r\n\r\nIt is important to learn the prefixes in order to convert from one to another. The following can help!\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Common Unit Prefixes<\/caption>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">Prefix<\/th>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">Name<\/th>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">Exponent<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">P<\/td>\r\n<td style=\"width: 33.3333%;\">pico<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{-12}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">N<\/td>\r\n<td style=\"width: 33.3333%;\">nano<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{-9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">\u00b5<\/td>\r\n<td style=\"width: 33.3333%;\">micro<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{-6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">m<\/td>\r\n<td style=\"width: 33.3333%;\">milli<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{-3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">no prefix<\/td>\r\n<td style=\"width: 33.3333%;\">no prefix<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{0}=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">k<\/td>\r\n<td style=\"width: 33.3333%;\">kilo<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">M<\/td>\r\n<td style=\"width: 33.3333%;\">mega<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">G<\/td>\r\n<td style=\"width: 33.3333%;\">giga<\/td>\r\n<td style=\"width: 33.3333%;\">[latex]10^{9}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"padding-left: 40px;\"><\/p>\r\n\r\n<h3>Example<\/h3>\r\nEXPRESS 2 500 Volts in Kilovolts:\r\n<p style=\"padding-left: 40px;\">2 500 V = _______ kV<\/p>\r\nReplace the Prefixes with the appropriate powers of 10.\r\n<p style=\"padding-left: 40px;\">2 500 X (100 V) = _______ X (103) V<\/p>\r\nThe power of 10 on the right-hand side is bigger than the power of ten on the left.\r\n\r\nTo keep the equation balanced the coefficient must be reduced by the same factor. That is, divided by 103.\r\n\r\nTo divide by 103 , move the decimal point of the coefficient three places to the left\r\n<p style=\"padding-left: 40px;\">2 500 X 100 V =2.5 X 103 V\r\n2 500 = 2.5 kV<\/p>","rendered":"<p>Raising 10 to a power means multiplying 10 by itself a certain number of times. The number of times you multiply 10 is equal to the exponent. So, for example, 10 to the power of 3 means multiplying 10 by itself 3 times, resulting in the number 1000.<\/p>\n<p>This looks like 10<sup>3<\/sup> = 10 \u00d7 10 \u00d7 10 = 1000<\/p>\n<h2>Electrical Units<\/h2>\n<p>Electricians use quantities in very large numbers or very small numbers.<\/p>\n<ul>\n<li>Large Unit Example: Transmission lines transmit at voltages of 500,000 volts.<\/li>\n<li>Small Unit Example: Computers deal in currents of 0.000 000 001 amperes.<\/li>\n<\/ul>\n<p>It is very easy to miss a zero when writing the numbers out!<\/p>\n<p>The solution is to express all of the numbers in terms of POWER OF 10.<\/p>\n<p>Engineering notation uses only those powers of 10 with an exponent that is a multiple of three.<\/p>\n<p>Example: 10<sup>-9<\/sup> , 10<sup>-6<\/sup> , 10<sup>-3<\/sup> , 10<sup>3<\/sup> , 10<sup>6<\/sup><\/p>\n<p>Each one of these engineering metric notational values is associated with a prefix. Instead of writing a number with a large power of 10, a metric prefix which represents the multiplier is placed ahead of the UNIT.<\/p>\n<p>Example:<\/p>\n<p>25 000 Volts = 25 \u00d7 103 Volts = 25 Kilovolts = <strong>25 kV<\/strong> (the kilo represents 103)<\/p>\n<p>It is important to learn the prefixes in order to convert from one to another. The following can help!<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<caption>Common Unit Prefixes<\/caption>\n<tbody>\n<tr>\n<th style=\"width: 33.3333%;\" scope=\"col\">Prefix<\/th>\n<th style=\"width: 33.3333%;\" scope=\"col\">Name<\/th>\n<th style=\"width: 33.3333%;\" scope=\"col\">Exponent<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">P<\/td>\n<td style=\"width: 33.3333%;\">pico<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{-12}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">N<\/td>\n<td style=\"width: 33.3333%;\">nano<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{-9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">\u00b5<\/td>\n<td style=\"width: 33.3333%;\">micro<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{-6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">m<\/td>\n<td style=\"width: 33.3333%;\">milli<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{-3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">no prefix<\/td>\n<td style=\"width: 33.3333%;\">no prefix<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{0}=1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">k<\/td>\n<td style=\"width: 33.3333%;\">kilo<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">M<\/td>\n<td style=\"width: 33.3333%;\">mega<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">G<\/td>\n<td style=\"width: 33.3333%;\">giga<\/td>\n<td style=\"width: 33.3333%;\">[latex]10^{9}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"padding-left: 40px;\">\n<h3>Example<\/h3>\n<p>EXPRESS 2 500 Volts in Kilovolts:<\/p>\n<p style=\"padding-left: 40px;\">2 500 V = _______ kV<\/p>\n<p>Replace the Prefixes with the appropriate powers of 10.<\/p>\n<p style=\"padding-left: 40px;\">2 500 X (100 V) = _______ X (103) V<\/p>\n<p>The power of 10 on the right-hand side is bigger than the power of ten on the left.<\/p>\n<p>To keep the equation balanced the coefficient must be reduced by the same factor. That is, divided by 103.<\/p>\n<p>To divide by 103 , move the decimal point of the coefficient three places to the left<\/p>\n<p style=\"padding-left: 40px;\">2 500 X 100 V =2.5 X 103 V<br \/>\n2 500 = 2.5 kV<\/p>\n","protected":false},"author":2001,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-182","chapter","type-chapter","status-publish","hentry"],"part":172,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/users\/2001"}],"version-history":[{"count":5,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/182\/revisions"}],"predecessor-version":[{"id":916,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/182\/revisions\/916"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/parts\/172"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapters\/182\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/media?parent=182"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/pressbooks\/v2\/chapter-type?post=182"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/contributor?post=182"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/wp-json\/wp\/v2\/license?post=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}