Fractions–decimals–percentages | Year 7

01 / LEARN

The idea, step by step

Percent means per hundred

A percentage states a count out of one hundred equal parts. Thirty-seven percent means 37 hundredths, not 37 whole units. A hundred-square grid makes the shared whole visible.

Fractions, decimals and percentages can describe the same proportion. Convert a fraction to hundredths when convenient, or divide to find its decimal value and then multiply by 100 to express the percentage.

Keep the whole consistent

To change a decimal to a percentage, multiply its numerical value by 100 and write the percent symbol. To change a percentage to a decimal, divide by 100. More than 100 percent represents more than one whole.

Write the exact simplified fraction when one is available. When comparing representations, convert them to one form rather than comparing their printed numbers. For example, 0.8 is 80 percent, so it exceeds 65 percent.

A common trap

0.6 is the same as 0.6 percent.

Instead: $0.6 = 60 %$ . The percent symbol already means division by 100, so $0.6 % = 0.006$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Use hundredths

Write $\frac{3}{5}$ as a decimal and a percentage.

$\frac{3}{5} = \frac{60}{100}$ .
60 hundredths is 0.60.
60 out of 100 is 60 percent.

0.6 = 60 %

Example 2

Convert a small percentage

Write $8 %$ as a decimal and a simplified fraction.

$8 % = \frac{8}{100}$ .
Dividing by 100 gives 0.08.
Simplify $\frac{8}{100}$ by 4 to obtain $\frac{2}{25}$ .

0.08 = \frac{2}{25}

Check your understanding

Write $\frac{3}{4}$ as a percentage.

Show answer

$75 %$

$\frac{3}{4} = \frac{75}{100}$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Write $\frac{7}{20}$ as a decimal and percentage.
2 marks
Write 0.45 as a percentage and simplified fraction.
2 marks
Write $125 %$ as a decimal and an improper fraction.
2 marks
Which is largest: $0.72$ , $\frac{3}{4}$ or $70 %$ ?
2 marks
Use the supplied hundred-square grid. Write the shaded share as a fraction, decimal and percentage.
2 marks
Tess says $40 % = 40$ . Explain why she is wrong.
3 marks

Read the worked solutions

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

Write $\frac{7}{20}$ as a decimal and percentage.
2 marks
$\frac{7}{20} = \frac{35}{100}$ .
$0.35 = 35 %$
Write 0.45 as a percentage and simplified fraction.
2 marks
$0.45 = \frac{45}{100} = \frac{9}{20}$ .
$45 % = \frac{9}{20}$
Write $125 %$ as a decimal and an improper fraction.
2 marks
$125 % = \frac{125}{100} = \frac{5}{4} = 1.25$ .
$1.25 = \frac{5}{4}$
Which is largest: $0.72$ , $\frac{3}{4}$ or $70 %$ ?
2 marks
They equal 72 percent, 75 percent and 70 percent.
$\frac{3}{4}$
Use the supplied hundred-square grid. Write the shaded share as a fraction, decimal and percentage.
2 marks
There are 100 equal squares and 37 are shaded.
$\frac{37}{100}$ , $0.37$ , $37 %$
Tess says $40 % = 40$ . Explain why she is wrong.
3 marks
Percent means out of 100, so $40 % = \frac{40}{100} = 0.4$ .
$40 % = 0.4$ , not 40.

Checking saved progress…

Continue learning

Percentages of quantities

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Fractions–decimals–percentages; percentages of quantities; expressing one amount as a percentage of another; discounts and sale prices; practical spending/budget comparisons; choosing and explaining a financial model.

Official curriculum source ↗

Back to Percentages and money