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Year 7

Converting fractions to recurring decimals

I can divide the numerator of a fraction by its denominator and know that this results in an equivalent recurring decimal.

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Year 7

Converting fractions to recurring decimals

I can divide the numerator of a fraction by its denominator and know that this results in an equivalent recurring decimal.

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Lesson details

Key learning points

  1. Dividing the numerator by the denominator may result in an equivalent recurring decimal.
  2. It can be shown that 1/9, 1/11 and 1/36 have equivalent recurring decimals.
  3. Using a calculator can help investigate fractions which are equivalent to terminating decimals.
  4. Using a calculator can help investigate fractions which convert to recurring decimals.

Keywords

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

Common misconception

Converting a fraction to a recurring decimal and then rounding the decimal, gives an accurate answer

The use of fractions is more preferred for accuracy than decimals. e.g 1/3 + 1/3 + 1/3 is not 0.3 + 0.3 + 0.3


To help you plan your year 7 maths lesson on: Converting fractions to recurring decimals, download all teaching resources for free and adapt to suit your pupils' needs...

Get pupils to think if we can multiply a recurring decimal by a number to make it a terminating decimal. Give 1/3, 3/11, 7/9 and 53/154. This thinking task deepens understanding of cancelling prime factors which are not 2 and/or 5.
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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.
Terminating decimals have a number of digits after the decimal point.
Correct Answer: finite
Q2.
Without using a calculator, work out the decimal value of $$\frac {13}{20}$$.
Correct Answer: 0.65, 0,65, .65, ,65
Q3.
Select all the fractions that can be written as terminating decimals.
$$\frac {11}{15}$$
Correct answer: $$\frac {11}{4}$$
Correct answer: $$\frac {11}{8}$$
Correct answer: $$\frac {11}{50}$$
$$\frac {11}{30}$$
Q4.
Aisha uses her calculator to convert $$0.668$$ to a fraction. She gets an answer of $$\frac {167}{\square}$$. What number should go in the square?
Correct Answer: 250
Q5.
Match each fraction to its terminating decimal. You can use a calculator for this question.
Correct Answer:$$\frac {73}{160}$$ ,$$0.45625$$
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$$0.45625$$

Correct Answer:$$\frac {57}{125}$$ ,$$0.456$$
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$$0.456$$

Correct Answer:$$\frac {63}{140}$$ ,$$0.45$$
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$$0.45$$

Correct Answer:$$\frac {2281}{5000}$$ ,$$0.4562$$
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$$0.4562$$

Correct Answer:$$\frac {34}{85}$$ ,$$0.4$$
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$$0.4$$

Q6.
Sam says that $$231 \over 330$$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Sam is correct or not.
Sam is correct as $$330$$ has factors of $$3$$ and $$11$$
Sam is correct as only fractions with a denominator of $$10$$ terminate
Sam is wrong as $$330$$ is a multiple of $$10$$
Correct answer: Sam is wrong as the fraction simplifies to $$7\over10$$ which terminates

Exit quiz

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6 Questions

Q1.
A decimal with an infinite repeating pattern of digits is called a decimal.
Correct Answer: recurring
Q2.
Match each decimal given using dot notation to its equivalent decimal.
Correct Answer:$$0. \dot 1 \dot 2$$ ,$$0.12121212...$$
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$$0.12121212...$$

Correct Answer:$$0. 1 2 \dot 3$$ ,$$0.123333333...$$
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$$0.123333333...$$

Correct Answer:$$0. \dot{1} 2 \dot {3}$$ ,$$0.123123123...$$
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$$0.123123123...$$

Correct Answer:$$0. \dot 1$$ ,$$0.111111111...$$
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$$0.111111111...$$

Correct Answer:$$0. 1\dot 2 \dot 3$$ ,$$0.123232323...$$
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$$0.123232323...$$

Q3.
Select all the fractions which are equivalent to a recurring decimal.
Correct answer: $$\frac{1}{3}$$
Correct answer: $$\frac{1}{12}$$
$$\frac{3}{24}$$
$$\frac{6}{15}$$
Correct answer: $$\frac{10}{12}$$
Q4.
Use short division to write $$8\over15$$ as a decimal.
$$0.53$$
$$0.53333333333$$
Correct answer: $$0.5 \dot3$$
$$0. \dot5 \dot3$$
Q5.
Jacob uses his calculator to write $$11\over12$$ as a decimal. His calculator display shows the number $$0.9166666667$$. Jacob says, "This shows my fraction terminates." Is Jacob correct? Explain why.
Yes; Jacob's number has 10 digits after the decimal point so it terminates.
Yes; the last digit is 7 not 6 so it doesn't repeat. So it must terminate.
Correct answer: No; the calculator only has a 12 digit display, the last 6 is rounded up to 7.
No; all decimals recur eventually.
Q6.
Izzy writes the recurring decimal $$0.71\dot6$$ as the fraction $$\frac{\square}{60}$$. What number should she write in the square?
Correct Answer: 43