Converting between fractions and decimals | Year 7

01 / LEARN

The idea, step by step

Denominators of ten, a hundred and a thousand

A terminating decimal names a count of place-value parts. For example, 0.37 is 37 hundredths. Write the matching fraction and simplify it by a common factor.

For many fractions, multiplying the denominator to a power of ten is a quick conversion. An eighth becomes 125 thousandths; a twentieth becomes five hundredths.

The fraction bar means division

Dividing the numerator by the denominator also converts the fraction. Keep zero placeholders and use a remainder to continue the division. A repeating remainder produces repeating digits.

A rounded decimal is an approximation, not an exact equality. Write an approximation sign if a value has been rounded and say how accurate it is. Exact terminating decimals can be used with an equals sign.

A common trap

Put the numerator after the decimal point to convert a fraction.

Instead: The denominator determines the size of each part. Three eighths is 0.375, not 0.3 or exactly 0.38.

02 / WORKED EXAMPLES

See the thinking

Example 1

Make hundredths

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

$\frac{7}{20} = \frac{35}{100}$ by multiplying both parts by 5.
35 hundredths is 0.35.

0.35

Example 2

Name the decimal parts

Write 0.375 as a simplified fraction.

$0.375 = \frac{375}{1000}$ .
Divide both by 125 to obtain $\frac{3}{8}$ .

\frac{3}{8}

Check your understanding

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

Show answer

0.36

$\frac{9}{25} = \frac{36}{100}$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF 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 ↗

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