Grade 10 Maths · Algebra

Convert recurring decimals to fractions

Change a recurring decimal into a fraction by multiplying by a power of 10 and subtracting (for example 0,333… = 1/3).

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Grade 10 Maths Writing a recurring decimal as fractionMiss Martins Maths and Science

Grade 10 | Recurring Decimal to Fractionmaths with ms m

Recurring decimals to fractions - Corbettmathscorbettmaths

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Question 1.2 · March 2025 · Provincial · 3 marks

1.2 Write

0, 13

(with 13 recurring) as a fraction, clearly show all your steps.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: convert recurring decimals to fractions

Work each one out first, then open the memo and check every tick.

3. Question WE3 · Siyavula Grade 10 Mathematics, 1.3 Rational and irrational numbers, Worked example 3 · 3 marks
WE3 Write $5, \dot{4} \dot{3} \dot{2}$ as a rational fraction.(3)
Show the memo (3 ticks)Memo
1. ✓
  Multiply by 1 000Let $x = 5, 432432432 \dots$
  $1000 x = 5432, 432432432 \dots$
  1 mark · Convert recurring decimals to fractions
2. ✓
  Subtract $1000 x - x = 5432, 432432 \dots - 5, 432432 \dots$
  $999 x = 5427$
  1 mark · Convert recurring decimals to fractions
3. ✓
  Answer $x = \frac{5 427}{999} = \frac{201}{37} = 5 \frac{16}{37}$
  1 mark · Convert recurring decimals to fractions
4. Question WE2 · Siyavula Grade 10 Mathematics, 1.3 Rational and irrational numbers, Worked example 2 · 3 marks
WE2 Write $0, \dot{3}$ in the form $\frac{a}{b}$ (where $a$ and $b$ are integers).(3)
Show the memo (3 ticks)Memo
1. ✓
  Multiply by 10Let $x = 0, 33333 \dots$
  $10 x = 3, 33333 \dots$
  1 mark · Convert recurring decimals to fractions
2. ✓
  Subtract $10 x - x = 3, 33333 \dots - 0, 33333 \dots$
  $9 x = 3$
  1 mark · Convert recurring decimals to fractions
3. ✓
  Answer $x = \frac{3}{9} = \frac{1}{3}$
  1 mark · Convert recurring decimals to fractions

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