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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 6 of 18
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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.
Lesson details
Key learning points
- Dividing the numerator by the denominator may result in an equivalent recurring decimal.
- It can be shown that 1/9, 1/11 and 1/36 have equivalent recurring decimals.
- Using a calculator can help investigate fractions which are equivalent to terminating decimals.
- 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
6 Questions
Q1.Terminating decimals have a number of digits after the decimal point.
Terminating decimals have a number of digits after the decimal point.
Correct Answer: finite
finite
Q2.Without using a calculator, work out the decimal value of $$\frac {13}{20}$$.
Without using a calculator, work out the decimal value of $$\frac {13}{20}$$.
Correct Answer: 0.65, 0,65, .65, ,65
0.65, 0,65, .65, ,65
Q3.Select all the fractions that can be written as terminating decimals.
Select all the fractions that can be written as terminating decimals.
$$\frac {11}{15}$$
Correct answer: $$\frac {11}{4}$$
$$\frac {11}{4}$$
Correct answer: $$\frac {11}{8}$$
$$\frac {11}{8}$$
Correct answer: $$\frac {11}{50}$$
$$\frac {11}{50}$$
$$\frac {11}{30}$$
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?
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
250
Q5.Match each fraction to its terminating decimal. You can use a calculator for this question.
Match each fraction to its terminating decimal. You can use a calculator for this question.
Correct Answer:$$\frac {73}{160}$$ ,$$0.45625$$
$$\frac {73}{160}$$ - $$0.45625$$
Correct Answer:$$\frac {57}{125}$$ ,$$0.456$$
$$\frac {57}{125}$$ - $$0.456$$
Correct Answer:$$\frac {63}{140}$$ ,$$0.45$$
$$\frac {63}{140}$$ - $$0.45$$
Correct Answer:$$\frac {2281}{5000}$$ ,$$0.4562$$
$$\frac {2281}{5000}$$ - $$0.4562$$
Correct Answer:$$\frac {34}{85}$$ ,$$0.4$$
$$\frac {34}{85}$$ - $$0.4$$
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 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
Sam is wrong as the fraction simplifies to $$7\over10$$ which terminates
Assessment exit quiz
6 Questions
Q1.A decimal with an infinite repeating pattern of digits is called a decimal.
A decimal with an infinite repeating pattern of digits is called a decimal.
Correct Answer: recurring
recurring
Q2.Match each decimal given using dot notation to its equivalent decimal.
Match each decimal given using dot notation to its equivalent decimal.
Correct Answer:$$0. \dot 1 \dot 2$$ ,$$0.12121212...$$
$$0. \dot 1 \dot 2$$ - $$0.12121212...$$
Correct Answer:$$0. 1 2 \dot 3$$ ,$$0.123333333...$$
$$0. 1 2 \dot 3$$ - $$0.123333333...$$
Correct Answer:$$0. \dot{1} 2 \dot {3}$$ ,$$0.123123123...$$
$$0. \dot{1} 2 \dot {3}$$ - $$0.123123123...$$
Correct Answer:$$0. \dot 1$$ ,$$0.111111111...$$
$$0. \dot 1$$ - $$0.111111111...$$
Correct Answer:$$0. 1\dot 2 \dot 3$$ ,$$0.123232323...$$
$$0. 1\dot 2 \dot 3$$ - $$0.123232323...$$
Q3.Select all the fractions which are equivalent to a recurring decimal.
Select all the fractions which are equivalent to a recurring decimal.
Correct answer: $$\frac{1}{3}$$
$$\frac{1}{3}$$
Correct answer: $$\frac{1}{12}$$
$$\frac{1}{12}$$
$$\frac{3}{24}$$
$$\frac{6}{15}$$
Correct answer: $$\frac{10}{12}$$
$$\frac{10}{12}$$
Q4.Use short division to write $$8\over15$$ as a decimal.
Use short division to write $$8\over15$$ as a decimal.
$$0.53$$
$$0.53333333333$$
Correct answer: $$0.5 \dot3$$
$$0.5 \dot3$$
$$0. \dot5 \dot3$$
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.
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; 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?
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
43
