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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

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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

The line in a fraction means divide.
Dividing the numerator by the denominator may result in an equivalent terminating decimal.
It can be shown that 1/2, 1/4 and 1/10 have equivalent terminating decimals.
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.

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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).

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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? £

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

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

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

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

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

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 $$2$$

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

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Converting fractions to terminating decimals

Converting fractions to terminating decimals

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

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

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

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

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

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? £

Assessment exit quiz

6 Questions

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

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

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

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?

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

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.

Lesson appears in

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

Maths

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

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

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

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

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

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? £

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

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

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

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?

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

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.