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Year 10
Higher

Converting any recurring decimal to a fraction

I can appreciate the infinite nature of recurring decimals and can convert between a recurring decimal and a fraction.

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Year 10
Higher

Converting any recurring decimal to a fraction

I can appreciate the infinite nature of recurring decimals and can convert between a recurring decimal and a fraction.

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Lesson details

Key learning points

  1. A recurring decimal does not terminate.
  2. By considering the infinite nature of recurring decimals, it is possible to create two equations.
  3. These simultaneous equations can be combined to create a third valid equation.
  4. This can be solved to find the fractional equivalent to the recurring decimal.
  5. A calculator can help us investigate this conversion.

Keywords

  • Recurring decimal - A recurring decimal is one that has an infinite number of digits after the decimal point.

  • Irrational number - An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0.

  • Terminating decimal - A terminating decimal is one that has a finite number of digits after the decimal point.

Common misconception

Assuming that the decimal part of the number will entirely disappear in the subtraction step.

Ensure that pupils line up the decimal points and use squares in their books for each digit. This should allow pupils to see the parts that cancel each other out and what is left when finding the difference.


To help you plan your year 10 maths lesson on: Converting any recurring decimal to a fraction, download all teaching resources for free and adapt to suit your pupils' needs...

Use MWB to quickly check that the pupils understand how to write different recurring decimals when given using the dot notation. They should be encouraged to write at least 6 digits after the decimal point.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Calculate 0.32 × 0.12
Correct Answer: 0.0384
Q2.
Calculate 0.36 ÷ 0.12
Correct Answer: 0.0432
Q3.
Calculate 0.32 × 0.9
Correct Answer: 0.288
Q4.
Calculate 0.04 - 1.23
Correct Answer: -1.19
Q5.
Which fraction is largest?
$$\frac{3}{7}$$
$$\frac{9}{21}$$
Correct answer: $$\frac{7}{12}$$
Q6.
Which fraction is smallest?
$$\frac{1}{10}$$
$$\frac{2}{21}$$
Correct answer: $$\frac{3}{33}$$

Exit quiz

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6 Questions

Q1.
Which of these fractions is equivalent to $$0.\dot{3}$$?
$$\frac{3}{10}$$
Correct answer: $$\frac{1}{3}$$
$$\frac{3}{90}$$
Q2.
Which of these fractions is equivalent to $$0.\dot{0}\dot{9}$$?
Correct answer: $$\frac{1}{11}$$
$$\frac{9}{11}$$
$$\frac{1}{90}$$
Q3.
Which of these fractions is equivalent to $$0.8\dot{3}$$?
$$\frac{8}{3}$$
$$\frac{83}{10}$$
Correct answer: $$\frac{5}{6}$$
Q4.
Which of these fractions is equivalent to $$0.08\dot{3}$$?
Correct answer: $$\frac{1}{12}$$
$$\frac{83}{10}$$
$$\frac{5}{6}$$
Q5.
Which of these fractions is equivalent to $$0.\dot{5}$$?
$$\frac{5}{10}$$
$$\frac{5}{11}$$
Correct answer: $$\frac{5}{9}$$
Q6.
Which of these fractions is equivalent to $$0.0\dot{6}$$?
Correct answer: $$\frac{1}{15}$$
$$\frac{1}{6}$$
$$\frac{1}{60}$$