Unit 17 Section 2 : Converting Fractions to Decimals

In this section we look at how to write fractions as decimals.

Method 1
If the fraction has 10, 100 or 1000 as the denominator, we can reverse the process we used to convert decimals to fractions.

You should already know that:

To convert to a decimal, we need to write 37 so that the last digit appears in the hundredths column, i.e. 0.37.

From this we can see that:

Method 2
If the fraction isn't like the one above, we may be able to change it to an equivalent fraction which does
have 10, 100 or 1000 as the denominator. The fractions can then be converted in the same way as before.

Look at the examples below:

Method 3
Sometimes we are not able to find an equivalent fraction which has 10, 100 or 1000 as the denominator.
In these cases, we need to divide the numerator by the denominator.

For example, we saw before that converts to 0.37
If we calculate 37 100, we also get the answer 0.37

So, to write as a decimal, we need to calculate 5 8:

So = 0.625 as a decimal.

Practice Questions
Convert each of these fractions into decimals, then click Click on this button below to see the correct answer to see whether you are correct.
(a)
(b)
(c)

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

NOTE: Do not use a calculator in any of these questions.

Question 1
Write these fractions as decimals:

(a)
3
=
10
(b)
7
=
100
(c)
9
=
1000
(d)
13
=
100
(e)
131
=
1000
(f)
47
=
1000
(g)
21
=
100
(h)
183
=
1000
(i)
19
=
100
(j)
19
=
1000
(k)
11
=
100
(l)
81
=
1000

Question 2
Find the missing numbers in the equivalent fractions:

(a)
1
=
2
10
(b)
7
=
20
100
(c)
2
=
25
100
(d)
1
=
4
100
(e)
2
=
50
100
(f)
64
=
500
1000
(g)
8
=
25
100
(h)
23
=
20
100

Question 3
Write these fractions as decimals:

(a)
1
=
2
(b)
4
=
5
(c)
9
=
50
(d)
3
=
25
(e)
3
=
20
(f)
3
=
500
(g)
1
=
250
(h)
7
=
20
(i)
61
=
200
(j)
18
=
25
(k)
9
=
125
(l)
1
=
4

Question 4
Write these improper fractions as decimals:

(a)
12
=
10
(b)
212
=
100
(c)
5218
=
1000
(d)
2008
=
100
(e)
2008
=
1000
(f)
418
=
10

Question 5
Write these improper fractions as decimals:

(a)
7
=
2
(b)
21
=
20
(c)
33
=
20
(d)
31
=
25
(e)
16
=
5
(f)
1001
=
500

Question 6
(a) Calculate 7 8.

(b) Write as a decimal.

Question 7
(a) Calculate 41 5.

(b) Write as a decimal.

Question 8
Write as a decimal.

Question 9
Write as a decimal.


You have now completed Unit 17 Section 2
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Produced by A.J.Reynolds January 2001