# How to Do Long Division with Decimals

## What Is Long Division with Decimals?

Long division is a method for dividing numbers.

Long division can be used for numbers with digits after the decimal point.

The long division below shows what we mean by using a number with digits after the decimal point:

In this long division, 8.4 has a digit (4) after a decimal point (.).

It is possible to use long division to divide into a decimal, divide by a decimal, and both together.

## How to Divide *Into* a Decimal

Long division can be used when the number being divided *into* (called the dividend) has a decimal point within it.

### Question

Divide the numbers below.

### Step-by-Step:

# 1

Identify the number being *divided* (called the dividend) and the number you are *dividing by* (called the divisor).

# 2

Write the dividend inside the *long division bracket* and the divisor outside to its left:

# 3

Divide the first digit of the dividend (8) by the divisor (4). Do not count remainders.

8 ÷ 4 = 2

4 goes into 8 **2** times.

# 4

Write the answer (2) above the long division bracket.

# 5

Multiply the answer from **Step 3** (2) with the divisor (4).

2 × 4 = 8

Write the answer underneath the digit divided into:

# 6

Subtract the bottom number (8) from the top number (8).

8 − 8 = 0

# 7

**The decimal point has been reached in the dividend.**

Place a decimal point above the long division bracket, directly above the decimal point in the dividend.

# 8

Bring down the next digit of the dividend (4).

# 9

Divide this number (4) by the divisor (4). Do not count remainders.

4 ÷ 4 = 1

4 goes into 4 **1** time.

# 10

Write the answer (1) above the long division bracket.

# 11

Multiply the answer from **Step 9** (1) with the divisor (4).

1 × 4 = 4

Write the answer underneath the number divided into:

# 12

Subtract the bottom number (4) from the top number (4).

4 − 4 = 0

There are no more digits to bring down.

### Answer:

The solution to 8.4 ÷ 4 is 2.1

## How to Divide *By* a Decimal

Long division can be used when the number you are dividing *by* (called the divisor) has a decimal point within it.

### Question

Divide the numbers below.

### Step-by-Step:

# 1

Identify the number being *divided* (called the dividend) and the number you are *dividing by* (called the divisor).

# 2

Count how may digits there are after the decimal point in the divisor (0.2).

There is 1 digit after the decimal point.

# 3

**To do the division, we want the divisor to be a whole number.**

Move the decimal point in the divisor right by as many places (1) as there are digits after it (as found in **Step 2**).

# 4

**To keep the division the same, move the decimal point the same number of places to the right in the dividend.**

Move the decimal point in the dividend right by the same number of places.

**Don't forget:** if there is a number without a decimal point, moving the decimal point a number of places to the right is the same as adding the same number of **0**s to the end of the number.

# 5

The long division has become:

# 6

Write the new dividend inside the *long division bracket* and the new divisor outside to its left:

# 7

Divide the first digit of the dividend (4) by the divisor (2). Do not count remainders.

4 ÷ 2 = 2

2 goes into 4 **2** times.

# 8

Write the answer (2) above the long division bracket.

# 9

Multiply the answer from **Step 7** (2) with the divisor (2).

2 × 2 = 4

Write the answer underneath the digit divided into:

# 10

Subtract the bottom number (4) from the top number (4).

4 − 4 = 0

# 11

Bring down the next digit of the dividend (0).

# 12

Divide this number (0) by the divisor (2). Do not count remainders.

0 ÷ 2 = 0

2 goes into 0 **0** times.

# 13

Write the answer (0) above the long division bracket.

# 14

Multiply the answer from **Step 12** (0) with the divisor (2).

0 × 2 = 0

Write the answer underneath the number divided into:

# 15

Subtract the bottom number (0) from the top number (0).

0 − 0 = 0

There are no more digits to bring down.

### Answer:

The solution to 4 ÷ 0.2 is 20.