Equivalent - Numbers are equivalent if they have exactly the same value.
Tenth - When one whole is divided into 10 equal parts, each part is one tenth. This can be expressed as a fraction or as a decimal.
Hundredth - When one whole is divided into 100 equal parts, each part is one hundredth. This can be expressed as a fraction or as a decimal.

Common misconception

The numbers in a decimal can be rewritten as a fraction so one-fifth becomes 1.5 as a decimal and that fractions and decimals do not represent equivalent values.

Read decimals as a number of tenths and hundredths to make the link to fractions.

Give pupils time to rehearse the fraction-decimal equivalences that are useful to have as known facts. Make the link to equivalent fractions and fractions in their simplest form when using tenths and hundredths to convert fractions into decimals.

Teacher tip

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Starter quiz

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6 Questions

Q1.

What is 100 divided into four equal parts? Each part is equal to

Correct Answer: 25, twenty five

Q2.

What is 1,000 divided into five equal parts? Each part is equal to

Correct Answer: 200

Q3.

What is 10 divided into five equal parts? Each part is equal to

Correct Answer: 2, two

Q4.

10 divided into five equal parts is the same as saying ___

Five times ten

Correct answer: One fifth of 10

Correct answer: 10 divided by 5

One fifth divided by 10

Correct answer: One fifth multiplied by 10

Q5.

Which equation would you use to calculate 1,000 divided into four equal parts?

$${1}\over{4}$$ ÷ 1,000

Correct answer: $${1}\over{4}$$ × 1,000

$${1}\over{5}$$ ÷ 1,000

$${1}\over{5}$$ × 1,000

Q6.

Match the statements to the equations they represent.

Correct Answer:$${1}\over{5}$$ × 10,One fifth of 10

One fifth of 10

Correct Answer:$${1}\over{4}$$ × 10,One quarter of 10

One quarter of 10

Correct Answer:$${1}\over{2}$$ × 10,One half of 10

One half of 10

Correct Answer:$${1}\over{10}$$ × 10,One tenth of 10

One tenth of 10

Exit quiz

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6 Questions

Q1.

How could you write this decimal as a fraction? The decimal is 0.04

$${1}\over{10}$$

$${1}\over{100}$$

$${2}\over{100}$$

Correct answer: $${4}\over{100}$$

Correct answer: $${2}\over{50}$$

Q2.

How could you write this decimal as a fraction? The decimal is 0.75

Correct answer: $${75}\over{100}$$

$${7}\over{10}$$

Correct answer: $${3}\over{4}$$

$${5}\over{100}$$

Q3.

Match the fraction with the equivalent decimal.

Correct Answer:$${3} \over {100}$$,0.03

0.03

Correct Answer:$${3} \over {4}$$,0.75

0.75

Correct Answer:$${3} \over {5}$$,0.6

0.6

Correct Answer:$${3} \over {10}$$,0.3

0.3

Q4.

Why is $${1}\over{3}$$ more difficult to convert to a decimal?

Correct answer: It is because 3 is not a factor of 10 or 100

It is because 3 is a prime number.

Q5.

Which pair of fractions and decimals is equivalent?

Correct Answer: An image in a quiz

Q6.

Which symbol would go between this fraction and decimal?

Correct answer: >

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