Multiplying and Dividing with Decimals

You might get a scary non-calculator question on multiplying or dividing using decimals. Luckily, these aren’t really any harder than the whole-number versions. You just need to know what to do in each case.

1) Start by ignoring the decimal points. Do the multiplication using whole numbers.

2) Count the total number of digits after the decimal points in the original numbers.

3) Make the answer have the same number of decimal places.

EXAMPLE
Work out 4.6 × 2.7

46 × 27 = 1242.

4.6 × 2.7 has 2 digits after the decimal points.

4.6 × 2.7 = 12.42, which is the product of the two numbers.

For these, you just set the question out like a whole-number division but put the decimal point in the answer right above the one in the question.

EXAMPLE
What is 52.8/3?

Put the decimal point in the answer above the one in the question.

3/52.8 = 3 into 5 goes once, carry the remainder of 2

3 into 22 goes 7 times, which gives us 21. Subtracting 21 from 22 leaves a remainder of 1. Next, we bring down the 8, making it 18.

3 into 18 goes 6 times so 52.8/3 = 17.6

Two-for-one here - this works if you’re dividing a whole number by a decimal, or a decimal by a decimal.

EXAMPLE
What is 36.6/0.12?

1) The trick here is to write it as a fraction. 36.6/0.12 = 36.6/0.12

2) Get rid of the decimals by multiplying top and bottom by 100 (see p.3): = 3660/12

3) It’s now a decimal-free division that you know how to solve:

12 into 3 won’t go so carry the 3

12 to 36 goes 3 times eactly

12 into 6 won’t go so carry the 6

12 into 60 goes 5 times exactly

So 36.6/0.12 = 305