Converting between fractions and decimals | Year 7

01 / LEARN

Understand the idea.

Denominators of ten, a hundred and a thousand

A terminating decimal names a whole-number count of tenths, hundredths or thousandths. For example, $0.37 = \frac{37}{100}$ . Read the last decimal place to choose the denominator, then simplify the resulting fraction if possible.

To convert in the other direction, seek an equivalent fraction with a power-of-ten denominator. Twentieths can become hundredths by multiplying by 5; eighths can become thousandths by multiplying by 125. Scale the numerator by the same factor.

The fraction bar means division

The fraction bar also means division: divide the numerator by the denominator. Continue through decimal places using zero placeholders. If the same remainder recurs, the division repeats the same pattern of digits rather than terminating.

Distinguish an exact decimal from a rounded display. For example, $\frac{1}{3} = 0.333 \dots$ , but $\frac{1}{3} \approx 0.33$ to two decimal places. Use an equals sign only when the written value is exactly the original amount.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Make hundredths

Write $\frac{7}{20}$ as a decimal.

Worked solution

1
Choose a hundredths denominator.
$20 \times 5 = 100$
Hundredths can be written directly with two decimal places.
2
Multiply the numerator by the same factor.
$\frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100}$
Scaling both parts equally keeps the fraction equivalent.
3
Read thirty-five hundredths.
$\frac{35}{100} = 0.35$
Three tenths and five hundredths give the exact terminating decimal.

Answer

0.35

EXAMPLE 02

Name the decimal parts

Write 0.375 as a simplified fraction.

Worked solution

1
Read the decimal in thousandths.
$0.375 = \frac{375}{1000}$
The last digit occupies the thousandths place.
2
Remove a common factor of 125.
$\frac{375}{1000} = \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}$
Three groups of 125 fit in 375 and eight fit in 1,000.
3
Check that the fraction is simplified.
$HCF (3, 8) = 1$
The numerator and denominator share no factor greater than 1.

Answer

$\frac{3}{8}$

03 / YOUR TURN

Try it yourself.

Check your understanding

Convert $\frac{9}{25}$ to a decimal.

Show answer & reasoning

0.36

Multiply numerator and denominator by 4: $\frac{9}{25} = \frac{36}{100} = 0.36$ . This is an exact conversion because the fraction has been renamed as hundredths.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Write $\frac{3}{10}$ as a decimal.
1 mark
Write $\frac{11}{20}$ as a decimal.
2 marks
Write $\frac{7}{8}$ as a decimal.
2 marks
Write 0.45 as a simplified fraction.
2 marks
Write 1.2 as an improper fraction and a mixed number.
2 marks
A calculator displays 0.666667 for $\frac{2}{3}$ . Is that an exact result? Explain.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Write $\frac{3}{10}$ as a decimal.
1 mark
Three tenths is 0.3.
0.3
Write $\frac{11}{20}$ as a decimal.
2 marks
$\frac{11}{20} = \frac{55}{100}$ .
0.55
Write $\frac{7}{8}$ as a decimal.
2 marks
$\frac{7}{8} = \frac{875}{1000}$ .
0.875
Write 0.45 as a simplified fraction.
2 marks
$\frac{45}{100} = \frac{9}{20}$ .
$\frac{9}{20}$
Write 1.2 as an improper fraction and a mixed number.
2 marks
$1.2 = \frac{12}{10} = \frac{6}{5}$ .
$\frac{6}{5} = 1 \frac{1}{5}$
A calculator displays 0.666667 for $\frac{2}{3}$ . Is that an exact result? Explain.
3 marks
Dividing 2 by 3 produces repeating sixes. The displayed result stops after a finite number of digits.
No; it is a rounded approximation.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Equivalent fractions and mixed numbers; ordering rational numbers on number lines; adding/subtracting fractions; multiplying/dividing fractions; four operations with decimals; converting between fractions and decimals; multi-step problems and checking estimates.

Official curriculum source ↗

In this lesson

Understand the idea.

Denominators of ten, a hundred and a thousand

The fraction bar means division

See the method in action.

Make hundredths

Choose a hundredths denominator.

Multiply the numerator by the same factor.

Read thirty-five hundredths.

Name the decimal parts

Read the decimal in thousandths.

Remove a common factor of 125.

Check that the fraction is simplified.

Try it yourself.

Check your understanding

Keep practising