27 Decimal Review

The decimal system is based on powers of 10, so let’s take the WHOLE number 1 and divide it into ten parts. These are called tenths. Each of those tenths looks like 1/10. If we divide 1/10 the decimal equivalent is 0.1. If we divide 0.1 into tenths we have 1/100 or 0.01, which is called one-hundredth
Because 1/10 ÷ 10 = 1/10 X 1/10 = 1/100 = 0.01

Dividing and Multiplying Decimals

Any number can easily be divided or multiplied by 10 simply by moving the decimal point in the number. All numbers have a decimal point. If it is a whole number or integer such as 7, the decimal point falls after the number such as 7. If it is exactly 7, it can be written as 7.0. If you needed to multiply it by 10, you would move the decimal point to the right one place because 10 has one zero on it. So 10 × 7.0 would be 70.

To divide by ten or a power of ten, you move the decimal point to the left by the same number of places as the number of zeros or decimal places in the number you are dividing by.If a number already has a decimal point in it, start with that decimal point.

Multiplying Decimals Rule of Thumb

Multiply the whole numbers without the decimals to start.
4.22 × 3.1 = ?

Start with:
422 × 31 = 1302

Now, there are 2 decimal places in 4.22 and 1 decimal place in 3.1. This is a total of 3 decimal places. We then put three decimal places in 13082 and we finally get the answer: 13.082

Dividing Decimals Rule of Thumb

Divide the number as you normally would, using long division by a whole number.
9.24 ÷ 7.008 = 74

Rule: We cannot divide by a decimal, just whole numbers.

Here to make 7.008, we multiply it by 1000 (3 decimal places).

But, if we multiply the bottom by 1000, we must multiply the top by 1000.

Thus, 9.24/7.008 becomes 9.24/7.008 X1000/1000 = 9240/7008 = 1.3185

You want the divisor 7.008 to be by a whole number because we cannot divide by a decimal. So, you need to move thedecimal point 3 places to the right:

7008 – Now you need to move the decimal point for the dividend 3 places to the right:

9240 – In this case you have to add a zero to move it 3 places.

Now you divide 9240 by 7008 to get the answer:

Practice Questions

1. 0.3 × 0.008
2. 3.35 × 8
3. 45.8 × 6
4. 5/4 ÷ 0.8 (keep in mind: (a/b)÷(c/d) = (a/b) × (d/c) )
5. When a fraction is divided by 1, the quotient is equal to:
6. 90.16 ÷ 9.2