# Dividing decimals

Dividing decimals is similar to regular division with the exception that we need to pay attention to the location of the decimal point. Decimals are a base 10 numeration system. Because of this, we can multiply various decimal division problems by powers of 10 to simplify the problem or ensure that the divisor doesn't contain a decimal point. To divide decimals, use the following steps and refer to the examples below:

1. Count the number of digits that follow the decimal point in the divisor (if any). For example, if the divisor is 4.5, there is one digit, 5, so n = 1
2. Multiply the divisor by 10n. Given the divisor, 4.5,
• 4.5 × 101 = 45
3. Divide the numbers. If long division is necessary perform long division as you would normally, and write a decimal point in the quotient that is directly above its position in the dividend.

Examples

1. Solve 12.5 ÷ 0.25:

Since there are two digits after the decimal point in the divisor, n=2, and 102 = 100

(100)[12.5 ÷ 0.25] = 1250 ÷ 25 = 50

In this case, the numbers divide without a remainder, and we did not need to use long division.

2. Solve 15.625 ÷ 0.2:

n=1, 101 = 10, so

(10)[15.625 ÷ 0.2] = 156.25 ÷ 2

Using long division:

From this example, we see that long division using decimals is not very different from regular long division.

As long as we set up the division problem such that the divisor does not have any decimal places, we can theoretically find the solution to any decimal division problem using long division.