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Long Division with Decimals

(KS2, Year 5)

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:

long division with decimals

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. 8 point 4 divided by 4

Step-by-Step:

1

Identify the number being divided (called the dividend) and the number you are dividing by (called the divisor). 8_point_4 divided by 4 long division decimals step 1

8_point_4 divided by 4 long division decimals step 1

2

Write the dividend inside the long division bracket and the divisor outside to its left: 8_point_4 divided by 4 long division decimals step 2

3

Divide the first digit of the dividend (8) by the divisor (4). Do not count remainders. 8_point_4 divided by 4 long division decimals step 3

8 ÷ 4 = 2

4 goes into 8 2 times.

4

Write the answer (2) above the long division bracket. 8_point_4 divided by 4 long division decimals step 4

5

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

2 × 4 = 8

Write the answer underneath the digit divided into: 8_point_4 divided by 4 long division decimals step 5

6

Subtract the bottom number (8) from the top number (8). 8_point_4 divided by 4 long division decimals step 6

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_point_4 divided by 4 long division decimals step 7

8_point_4 divided by 4 long division decimals step 7

8

Bring down the next digit of the dividend (4). 8_point_4 divided by 4 long division decimals step 8

9

Divide this number (4) by the divisor (4). Do not count remainders. 8_point_4 divided by 4 long division decimals step 9

4 ÷ 4 = 1

4 goes into 4 1 time.

10

Write the answer (1) above the long division bracket. 8_point_4 divided by 4 long division decimals step 10

11

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

1 × 4 = 4

Write the answer underneath the number divided into: 8_point_4 divided by 4 long division decimals step 11

12

Subtract the bottom number (4) from the top number (4). 8_point_4 divided by 4 long division decimals step 12

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. 4 divided by 0 point 2

Step-by-Step:

1

Identify the number being divided (called the dividend) and the number you are dividing by (called the divisor). 4_divided_by 0 point 2 long division decimals step 1

4_divided_by 0 point 2 long division decimals step 1

2

Count how may digits there are after the decimal point in the divisor (0.2). 4_divided_by 0 point 2 long division decimals step 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_divided_by 0 point 2 long division decimals step 3

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. 4_divided_by 0 point 2 long division decimals step 4

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 0s 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: 4_divided_by 0 point 2 long division decimals step 6