# Dividing Decimals

You'll learn methods for dividing decimals by a whole number, by another decimal, and by a fraction. It's really easy once you get the hang of it, and it will repay your investment in time and effort many folds as you progress in learning Algebra.

## Decimal Division By A Whole Number

Dividing a decimal by a whole number can be done reliably (that is, with minimum chance of making mistakes) using long division. Of course, once you've had enough practice, you can use shorter and more advance techniques to get the answers faster.

You'll see how to do long division in the examples below. And yeah, be sure to line up the decimal points vertically.

Example
Divide the following.
(a) 73.8 ÷ 12
(b) 143.55 ÷ 15

Solution

Notice that the decimal points are in line. No mis-alignments like shown below.

## Decimal Division By A Decimal

When dividing a decimal with a decimal, we can reuse the techniques we learned from dividing a decimal by a whole number. Simply change the divisor (at the right side of the ÷) into a whole number first by multiplying both divisor and dividend with the same number, then proceed with the long division.

Example
Divide the following.
(a) 24.032 ÷ 16
(b) 0.304 8 ÷ 0.48
Solution
(a) First, convert the denominator (1.6) into a whole number by multiplying both the numerator (24.032) and denominator by 10.

Therefore, 24.032 ÷ 1.6 = 15.02

Therefore, 0.304 8 ÷ 0.48 = 0.635

## Decimal Division By The Powers of 10

Dividing decimals by powers of 10 (e.g. 0.001, 0.01, 0.1, 10, 100, 1000, and so on) is a special case. You can use long division to solve it, but it's not the fastest and most efficient way to do it. Here's a method that can only be used in this case.

When dividing a decimal with a power of 10, shift the decimal to the left according to the number of zeros in the power of 10. For instance,

When dividing a decimal with 0.1, 0.01 or 0.001, shift the decimal point to the right according to the number of decimal places in 0.1, 0.01 or 0.001. For instance,

Example
Divide the following.
(a) 2.033 ÷ 1000
(b) 19.253 ÷ 0.001

Solution
(a) 2.033 ÷ 1000 = 0.00233
(b) 19.253 ÷ 0.001 = 19253

## Here's a Tip...

When multiplying or dividing a decimal by a power of 10 (10, 100, 1000, …) or a decimal like 0.1, 0.01 or 0.001, the decimal point can be shifted as follows:

## Decimal Division By A Fraction

It's not difficult to divide a decimal by a fraction. You'll first need to change “÷” into “×”, `then change the fraction into its reciprocal. It's a fancy way of saying that you need to flip the fraction upside down (numerator becomes the denominator, and vice versa). Solve it after that. See the example below.

Example
Divide the following.

Solution

## Dividing Decimals Word Problems

Example
A rope is 32.16 m long. It is cut into identical pieces, each measuring 8.04 m long. How many pieces were cut from the rope?

Solution

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