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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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New
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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 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

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.
Teacher tip

Equipment

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This content is © Oak National Academy Limited (2024), 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.
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

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 $$2$$