Recurring decimals
Number
- Higher
- Non-calculator
- 8 questions
- 29 marks
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
-
Write $0.\dot{7}$ as a fraction in its simplest form.
2 marks
-
Write $\dfrac{5}{6}$ as a decimal.
2 marks
-
Write $0.\dot{1}\dot{6}$ as a fraction in its simplest form.
3 marks
-
Write $0.\dot{4}\dot{5}$ as a fraction in its simplest form.
3 marks
-
Write $0.2\dot{4}\dot{5}$ as a fraction in its simplest form.
4 marks
-
Prove that $0.4\dot{9} = 0.5$.
4 marks
-
Write $0.\dot{1}\dot{3}\dot{5}$ as a fraction in its simplest form.
5 marks
-
Write $0.\dot{3}\dot{6}$ as a fraction in its simplest form. Then write $0.2\dot{5}\dot{4}$ as a fraction in its simplest form.
6 marks
Mark scheme
-
Answer. $\dfrac{7}{9}$
- Let $x = 0.\dot{7}$. Then $10x - x = 7$.
- $x = \dfrac{7}{9}$
-
Answer. $0.8\dot{3}$
- $5 \div 6 = 0.8333\ldots$
- $0.8\dot{3}$
-
Answer. $\dfrac{16}{99}$
- Let $x = 0.\dot{1}\dot{6}$. Then $100x - x = 16$.
- $x = \dfrac{16}{99}$
-
Answer. $\dfrac{5}{11}$
- $\dfrac{45}{99}$
- $\dfrac{5}{11}$
-
Answer. $\dfrac{27}{110}$
- Let $x = 0.2\dot{4}\dot{5}$. Then $1000x - 10x = 243$.
- $x = \dfrac{243}{990} = \dfrac{27}{110}$.
-
Answer. $0.4\dot{9} = \dfrac{1}{2}$
- Let $x = 0.4\dot{9}$. Then $10x = 4.\dot{9}$ and $100x = 49.\dot{9}$.
- $90x = 45$, so $x = \dfrac{1}{2}$.
-
Answer. $\dfrac{5}{37}$
- Let $x = 0.\dot{1}\dot{3}\dot{5}$. Then $999x = 135$.
- $x = \dfrac{135}{999} = \dfrac{5}{37}$.
-
Answer. $\dfrac{4}{11}$ and $\dfrac{14}{55}$
- $0.\dot{3}\dot{6} = \dfrac{36}{99} = \dfrac{4}{11}$.
- For $0.2\dot{5}\dot{4}$, $1000x - 10x = 252$.
- $x = \dfrac{252}{990} = \dfrac{14}{55}$.