Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Recurring decimals as fractions

Using algebra to convert.

12 original questions, 34 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

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

  1. 0.3̇
  2. 0.8̇
2 marks
Show answer
a) 1/3 b) 8/9
2

Amelia says that 0.2̇9̇ = 29100

Explain why Amelia is wrong.

1 mark
Show answer
0.2̇9̇ means the digits 29 repeat forever, so it equals 0.292929... = 2999, not 29100. 29100 is the terminating decimal 0.29.
3

Express 0.7̇ as a fraction.

2 marks
Show answer
79
4

Express 0.5̇4̇ as a fraction in its simplest form.

3 marks
Show answer
611
5

Prove algebraically that the recurring decimal 0.4̇5̇ can be written as 511

3 marks
Show answer
Let x = 0.454545..., 100x = 45.454545..., 99x = 45, x = 4599 = 511
6

Express the recurring decimal 0.2̇13̇ as a fraction in its simplest form.

(The digits 2, 1 and 3 all recur.)

3 marks
Show answer
71333
7

Write 1.23̇ as a mixed number in its simplest form.

(Only the digit 3 recurs.)

3 marks
Show answer
1 730
8

Prove algebraically that the recurring decimal 0.28̇ can be written as 1345

(Only the digit 8 recurs.)

3 marks
Show answer
Let x = 0.2888..., 10x = 2.888..., 100x = 28.888..., 90x = 26, x = 2690 = 1345
9

Express the recurring decimal 0.35̇1̇ as a fraction in its simplest form.

(Only the digits 5 and 1 recur.)

3 marks
Show answer
58165
10

Work out 0.1̇3̇ + 0.5̇

Give your answer as a fraction in its simplest form.

3 marks
Show answer
6899
11

Show algebraically that 0.7̇2̇ + 0.2̇7̇ = 1

3 marks
Show answer
0.727272... = 7299 and 0.272727... = 2799; 7299 + 2799 = 9999 = 1
12

Work out 0.1̇8̇ × 0.4̇5̇

Give your answer as a fraction in its simplest form.

You must show all your working.

5 marks
Show answer
10121

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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