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Lesson 6 of 18

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 6 of 18
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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.

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

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.
Teacher tip

Licence

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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Prior knowledge 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:$$\frac {73}{160}$$ ,$$0.45625$$

$$0.45625$$

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

$$0.456$$

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

$$0.45$$

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

$$0.4562$$

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

$$0.4$$

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

Assessment 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:$$0. \dot 1 \dot 2$$ ,$$0.12121212...$$

$$0.12121212...$$

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

$$0.123333333...$$

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

$$0.123123123...$$

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

$$0.111111111...$$

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

$$0.123232323...$$

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

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UnitMaths / Comparing and ordering fractions and decimals (positive and negative)

Maths

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