Worksheets · Higher

Recurring decimals as fractions

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 4 marks

   Write each recurring decimal as a fraction in its simplest form.

   (a) $0.\dot{7}$ (2)

   (b) $0.\dot{2}\dot{7}$ (2)
2. Question 2Non-calculator · 5 marks

   $0.\dot{2} = \frac{2}{9}$

   (a) Use this fact to write $0.0\dot{2}$ as a fraction in its simplest form. (2)

   (b) Work out $0.\dot{3} + 0.0\dot{2}$. Give your answer as a fraction in its simplest form. (3)
3. Question 3Non-calculator · 3 marks

   (a) The digits a and b are non-zero. The decimal x = 0.ababab… repeats the two-digit block ab. The decimal y = 0.bababa… repeats the reversed block ba. Given x + y = 1 and x $-$ y = 3/11, find the two-digit integer ab. You must show your working. (3)