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Lesson 5 of 18
  • Year 7

Converting fractions to terminating decimals

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

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Lesson 5 of 18
New
New
  • Year 7

Converting fractions to terminating decimals

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

Download all

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Lesson details

Key learning points

  1. The line in a fraction means divide.
  2. Dividing the numerator by the denominator may result in an equivalent terminating decimal.
  3. It can be shown that 1/2, 1/4 and 1/10 have equivalent terminating decimals.
  4. Using a calculator can help investigate fractions which are equivalent to terminating decimals.

Keywords

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

Common misconception

Denominators that are multiples of 10 will give a terminating decimal.

Investigate the difference between powers of 10 and multiples of 10. e.g 7/30 and 7/100


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

After emphasising fractions must be in their simplest form and the denominator must have a product of its prime factors of 2 and/or 5, ask pupils to list as many non-terminating fractions in 1 minute where the denominator must be less than 100.
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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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Prior knowledge starter quiz

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6 Questions

Q1.
Fractions where the numerator is less than the denominator are called fractions.

Correct Answer: proper

Q2.
The integer that is equivalent to the fraction $$30 \over 5$$ is .

Correct Answer: 6, six

Q3.
Write $$3\frac{2}{7}$$ as an improper fraction.

$$\frac{23}{2}$$
$$\frac{21}{7}$$
$$\frac{22}{7}$$
Correct answer: $$\frac{23}{7}$$
$$\frac{24}{7}$$

Q4.
Write the correct symbol (<, > or =) to make the statement true: $$17 \frac {1}{2} $$ $$\frac {69}{4} $$

Correct Answer: >

Q5.
Starting with the smallest, put these fractions and mixed numbers in order of size.

1 - $$1\frac {1}{8} $$
2 - $$1\frac {1}{4} $$
3 - $$\frac {13}{8} $$
4 - $$1\frac {3}{4} $$
5 - $$2\frac {1}{8} $$
6 - $$\frac {18}{8} $$

Q6.
A gardener puts up a fence around a rectangular garden. Each fence panel is 1 metre long and costs £25. What is the total cost of the fencing? £

An image in a quiz
Correct Answer: 650, £650, 650.00, £650.00

Assessment exit quiz

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6 Questions

Q1.
Decimals that have a finite number of digits after the decimal point are called decimals.

Correct Answer: terminating

Q2.
Without using a calculator, work out the decimal value of $$\frac {7}{8}$$.

Correct Answer: 0.875, .875

Q3.
Select all the fractions that can be written as terminating decimals.

Correct answer: $$\frac {7}{16}$$
Correct answer: $$\frac {7}{5}$$
$$\frac {7}{15}$$
Correct answer: $$\frac {7}{20}$$
$$\frac {7}{30}$$

Q4.
Sofia uses her calculator to convert $$0.3756$$ to a fraction. She gets an answer of $$\frac {939}{\square}$$. What number should go in the square?

Correct Answer: 2500

Q5.
Match each fraction to its terminating decimal. You can use a calculator for this question.

Correct Answer:$$\frac {82}{125}$$ ,$$0.656$$

$$0.656$$

Correct Answer:$$\frac {3281}{5000}$$ ,$$0.6562$$

$$0.6562$$

Correct Answer:$$\frac {21}{32}$$,$$0.65625$$

$$0.65625$$

Correct Answer:$$\frac {26}{40}$$ ,$$0.65$$

$$0.65$$

Correct Answer:$$\frac {180}{300}$$ ,$$0.6$$

$$0.6$$

Q6.
Lucas says that $$66 \over 1320$$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Lucas is correct or not.

Lucas is correct as $$1320$$ has factors of $$3$$ and $$11$$
Lucas is correct as only fractions with a denominator of $$10$$ terminate
Correct answer: Lucas is wrong as the fraction simplifies to $$1\over20$$ which terminates
Lucas is wrong as the denominator is a multiple of $$10$$
Lucas is wrong as $$66$$ is a multiple of $$2$$