# 3.7 Multiplying and dividing with decimals

Multiplication and division of decimal numbers are carried out just as with whole numbers, except that now you can carry out the division even when one number does not divide exactly into the other. You also need to take care about the position of the decimal point. So check your answer is sensible.

## Example 18

(a) If somebody’s hair grows at the rate of 0.4 cm a week, how much will it grow in 52 weeks or one year?

(b) How long would it take to grow their hair 10 cm?

(c) How long would it take to grow their hair 3 cm?

### Answer

(a) In 52 weeks it grows 52 × 0.4 cm.

To multiply by 0.4, multiply by 4 and shift the digits one place to the right,

52 × 4 = 208. So 52 × 0.4 = 20.8.

So the hair will grow 20.8 cm in a year.

(0.4 is just under a half and half of 52 is 26, so the answer is sensible.)

**Notice that multiplying by 0.4 gives an answer smaller than 52.**

(b) You need to know how many times 0.4 cm goes into 10 cm, so divide 10 by 0.4,

10÷ 0.4 = = (multiply top and bottom by 10).

Now carry out the division: 100 ÷ 4 = 25.

So it would take 25 weeks to grow 10 cm.

(Check: 10 cm is about half of the previous answer of 20.8 cm which took a year, so will take about half a year. 25 weeks is near enough half a year, so the answer is sensible.)

(c) There are several ways of doing this. You might do it formally as

Carrying out the division gives 7.5.

Alternatively you might do it more informally: it grows 4 cm in 10 weeks,

and 3 cm is three-quarters of 4 cm,

so the answer is three-quarters of 10 weeks,

i.e. × 10 = 7.5 weeks.

Therefore it would take 7.5 weeks to grow 3 cm.

(Check: 3 cm is a bit less than a third of 10 cm which takes 25 weeks, so will take a bit less than a third of 25 weeks. 7.5 weeks is near enough a third of 25 weeks, so the answer is sensible.)