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MATHEMATICS
For
GCSE
Recurring Decimals
GCSE Higher Tier
Also
KS3 Middle & Top set
Denis Dalaba MSc, B.Ed.
©LearnMaths 2017 www.maths4maths.co.uk
by Denis Dalaba
1
Recurring decimals
Learning objective: To convert recurring decimals to
fractions
Starter
Calculate the following decimals
a. 3.6̇ – 2.6̇
b. 5.1̇2̇3̇ - 2.1̇2̇3̇
Activity 1
Convert the following recurring decimals to fractions
Case 1 (0.𝒏̇ )
Case 2 (0.𝒎̇𝒏)̇
0.3̇2̇
0.5̇
Case 3 (0.𝒂̇ 𝒃̇𝒄)̇
0.1̇2̇3̇
Case 4 (0.𝒂 𝒃̇𝒄)̇
0.24̇5̇
Case 5 (a.𝒃̇𝒄)̇
2.3̇4̇
Case 6 (a.𝒃𝒄̇ 𝒅)̇
2.12̇3̇
Case 7 (0.𝟎𝒃̇)
0.05̇
Case 8
Proof that 0.9̇ = 1
Activity 2
Write down your own generalisation of how to change recurring
decimals to fractions.
©LearnMaths 2017 www.maths4maths.co.uk
by Denis Dalaba
2
Exercise 1
1. Convert the following recurring decimals to fractions.
Write your answers in their lowest form.
a) 0.6̇
b)0.5̇7̇
c) 0.9̇2̇2̇
d)0.25̇9̇
e) 5.9̇8̇
f) 9.82̇7̇
g) 0.08̇
h)Proof that 0.9̇9̇ = 1
©LearnMaths 2017 www.maths4maths.co.uk
by Denis Dalaba
3
i) 0.7̇7̇
j) 1.1̇2̇6̇
k) 0.032̇
l) 1.8181818181
m)
n) 8.315315315
0.4546464646
2. Write the recurring decimal 0.1̇2̇2̇
𝑎
As a fraction in the form with a and b being integers.
𝑏
3. Put the numbers in ascending order
0.1̇2̇, 9/11, 11-1, √0.4̇
4. Evaluate 0.1̇2̇ + 0.1̇2̇2̇
5. Evaluate 7.1̇2̇3̇ - 1.1̇2̇2̇
6. Evaluate (0.2̇)2
Visit www.maths4maths.co.uk for the answers and
more exercises
©LearnMaths 2017 www.maths4maths.co.uk
by Denis Dalaba
4