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7.2 Converting fractions to decimals

7.2 Converting fractions to decimals

You already know how to convert a fraction to a decimal using equivalent fractions. You can also use
division to convert a fraction to a decimal.
6
The fraction is ‘six twenty-fifths’, ‘six out of twenty-five’ or ‘six divided by twenty-five’.
25
To work out the fraction as a decimal, divide 6 by 25: 6 ÷ 25 = 0.24
Use a calculator to do this.
The decimal 0.24 is a terminating decimal because it comes to an end.

When you convert the fraction 71 to a decimal you get: 71 ÷ 99 = 0.71717171…
99
The number 0.71717171… is a recurring decimal as the digits 7 and
1 carry on repeating forever. You can write 0.71717171… with A recurring decimal can always
the three dots at the end to show that the number goes on forever. You be written as a fraction.

can also write the number as 071. , with dots above the 7 and the 1,
to show that the 7 and 1 carry on repeating forever.

Worked example 7.2

Use division to convert each fraction to a decimal. In part c give your answer correct to 3 d.p.
3 5 3
a b c
8 11 7

a 3 ÷ 8 = 0.375 This answer is a terminating decimal, so write down all the digits.
b 5 ÷ 11 = 045. This answer is a recurring decimal, so write it as 045. or 0.4545….
c 3 ÷ 7 = 0.428571428… This answer is a recurring decimal as the digits 428571 are repeated, but
= 0.429 (3 d.p.) this time you are asked to round the number to three decimal places.

✦ Exercise 7.2

1 Use division to convert each of these fractions to a terminating decimal.

a 17 b 11 c 1 d 5 e 29
25 20 8 16 32
2 Use division to convert each of these fractions to a recurring decimal.

a 2 b 1 c 7 d 13 e 41
3 9 11 33 333
3 Use division to convert each of these fractions to a decimal, correct to three decimal places.
a 5 b 6 c 16 d 18 e 126
13 7 21 35 289

4 Sasha is told that 1 = 006 and that 1 = 0045.
.
.
15 22
Without using a calculator, she must match each 4 7 026 0318
.
.
15 22
red fraction card with its correct blue decimal card.

.
.
Sasha thinks that 4 = 026 and that 7 = 0318.
15 22
Do you think she is correct? Explain your answer.
7 Fractions 73