1. Year 9: Fractions to/from Decimals
Dr J Frost
Last modified: 24th November 2015

2. Converting between decimals and fractions
From non-recurring decimals to fractions…
0.024= = 6 250 ?
3.15= =3 3 20 ?

3. Quick Exercises
Express the following as fractions/mixed numbers in their simplest form (no calculators!).
0.005= = 1 200
0.48= = 12 25
1.875=1 7 8
2.248= =
5.765= ? 1 ? 2 ? 3 ? 4 ? 5

4. Converting between decimals and fractions
2 5 =0.4
3 16 =0.1875 ? ?
7 32 =
6 11 = ? ?
53 7 =
11 15 =0.7 3 ? ?
When will it not be a recurring decimal? ?
It the fraction in its simplest form only has prime factors of 2 and 5 in its denominator.

5. Exercise
Express as decimals (using recurring notation where appropriate)
1 13 =
1 7 =
22 21 =
17 12 =1.41 6
2 9 =0. 2
15 16 =0.9375
5 11 =
11 32 =
7 15 =0.4 6 ? ? 1 6 7 ? ? 2 ? ? 8 3 ? 4 ? 9 ? 5

6. Converting recurring decimals to fractions
Convert to a fraction.
𝑥= …
100𝑥= …
99𝑥=54
𝑥= = 6 11

7. Converting recurring decimals to fractions?
0.3 4 = 31 90 ? =
A* question alert! ?
= =

8. Card Sort
Match the recurring decimals to their corresponding fractions (no calculators permitted!)
0.123
0.12 3
41 333
37 300
61 495

9. Exercises
0. 5 = 5 9
0.4 3 = 13 30
= 68 99
1.2 7 = 23 18 =
= 13 33 ? =
= =
= =
= =
= = ? 1 7 2 ? ? 8 3 ? ? 9 4 ? ? 10 5 ? ? 11 ? 6
Given that = what is ?
If 𝟑 𝟏𝟏 =𝟎. 𝟐 𝟕 then 𝟎.𝟎 𝟐 𝟕 = 𝟑 𝟏𝟏𝟎
Thus𝟏.𝟑 𝟐 𝟕 =𝟏.𝟑+ 𝟑 𝟏𝟏𝟎 = 𝟕𝟑 𝟓𝟓 N ?