Long Division to Decimal Places

When we are given a long division to do it doesn't always work out to a whole number. Sometimes there are numbers left over. We can use the long division process to work out the answer to a number of decimal places.

The secret to working out a long division to decimal places is the ability to add zeros after the decimal point.

Example: 150 is the same as 150.00

We can add as many zeros as we wish after the decimal point without altering the numbers value.

We will use the example below. It works out neatly to one decimal place

435 ÷ 25

If you feel happy with the process on the long division page you can skip the first bit.

 

divide step 1 4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.
divide step 2   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 3 25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 4 4 – 0 = 4 Now we take away the bottom number from the top number.
divide step 5   Bring down the next number of the dividend.
divide step 6 43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.
divide step 7   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 8 25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
divide step 9 43 – 25 = 18 Now we take away the bottom number from the top number.
divide step 10   Bring down the next number of the dividend.
divide step 11 185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.
divide step 12   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 13 25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 14 185 – 175 = 10 Now we take away the bottom number from the top number.
divide step 15   Now we have reached the end of the whole numbers we add a decimal place and the first zero. Notice the decimal point which has appeared on the answer line and by the dividend. It does not appear anywhere else.
divide step 16   Bring down the next number of the dividend.
divide step 17 100 ÷ 25 = 4 remainder 0 Divide this number by the divisor.
divide step 18   The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 19 25 × 4 = 100 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 20 100 – 100 = 0 Now we take away the bottom number from the top number.
divide step 21  

The subtraction has given zero. We stop when this happens. The answer is 17.4 

As long as the subtraction gives a number above zero the long division can carry on to as many decimal places as we wish.

 

Answer: 435 ÷ 25 = 17.4