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## Dividing Decimals

#### Introduction

Dividing decimals is very similar to dividing whole numbers, although special attention needs to be given to the position of the decimal point.

#### Terms

Decimal Point - The decimal point looks like a period and is always placed after the “ones” position of a number.
Decimal Notation - Decimal notation is useful for writing numbers which are not whole numbers.
Whole Number - A whole number is a number with nothing but zeroes after the decimal point.

## Lesson

The most important thing to remember about dividing decimals is to make sure that the decimal place is in the right spot. You may think at first that $dfrac{.6}{.03}=.2$, but the correct answer is actually 20. To divide two decimals, first count the number of digits each number has after the decimal point. For example, .02 has two digits after the decimal point, .0034 has four digits, and .9999999 has 7 digits. Next, forget about the decimal place and divide the two numbers as if they were normal whole numbers. Finally, when finished, subtract the number of digits after the decimal in the first number by the number of digits after the decimal in the second number, and move the decimal that many places to the left. A negative number here means you will move the decimal point to the right. For example, let’s calculate $rac{.08}{.002}$. The number .08 has two digits after the decimal and .002 has three digits. Subtracting these numbers, we get $2-3=-1$, which means that we will have to move the decimal one space to the right in our final answer. Next, we forget about the decimals, and divide the two numbers normally. $rac{8}{2}=4$ Finally, move the decimal place one space to the right, and our final answer is 40.

### Alternative Method

Say you have $0.6/0.03$ – You would move the decimal point the same number of spaces to the right (enough to make whole numbers out of both the numbers) – so you get 60/3 (after multiplying top and bottom by 100) = 20 $rac{0.6}{0.03} * rac{100}{100} = rac{60}{3} = 20$.

In the case of 0.08/0.002 you would move the decimal place three places to get 80/2, then you divide as normal to get 40. $rac{0.08}{0.002} * rac{1000}{1000} = rac{80}{2} = 40$.

## Examples

#### Dividing Decimals (Example 1)

$0.6 \div 0.03$
$0.6 * 100 = 60$
$0.03 * 100 = 3$

#### Dividing Decimals (Example 2)

There are 2.54 centimeters in one inch. How many inches are there in 19.01 centimeters?
$19.01 * 100 = 1{,}901$
$2.54 * 100 = 254$