Fractions–decimals–percentages | Year 7

01 / LEARN

Understand the idea.

Percent means per hundred

Percent means “per hundred”. On a hundred-square grid, $37 %$ shades $37$ of the $100$ equal squares. The entire grid is the whole; the percentage tells us the share of that whole.

A fraction, decimal and percentage can name the same share. To convert a fraction, make an equivalent fraction with denominator $100$ when possible. Otherwise divide its numerator by its denominator to obtain a decimal.

Keep the whole consistent

A decimal counts wholes and parts of a whole; a percentage counts hundredths. Thus $0.8 = 80 %$ , whereas $0.8 % = 0.008$ . Multiply a decimal's numerical value by $100$ when writing it as a percentage, and divide by $100$ in the reverse direction.

Compare shares by first writing them in the same form. For the same whole, $0.8 = 80 %$ exceeds $65 %$ . A percentage above $100 %$ represents more than one whole, rather than an impossible value.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Use hundredths

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

Worked solution

1
Make hundredths.
$\frac{3}{5} = \frac{3 \times 20}{5 \times 20} = \frac{60}{100}$
Multiplying numerator and denominator by the same nonzero number preserves the fraction.
2
Read the decimal.
$\frac{60}{100} = 0.60 = 0.6$
Sixty hundredths is six tenths; the final zero does not change the value.
3
Write the percentage.
$\frac{60}{100} = 60 %$
A percentage states how many equal parts there are per hundred.

Answer

$0.6 = 60 %$

EXAMPLE 02

Convert a small percentage

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

Worked solution

1
Write the percentage as hundredths.
$8 % = \frac{8}{100}$
The percent sign means division by one hundred.
2
Read the decimal places.
$\frac{8}{100} = 0.08$
Eight hundredths requires a zero in the tenths place.
3
Simplify the fraction.
$\frac{8}{100} = \frac{8 \div 4}{100 \div 4} = \frac{2}{25}$
Dividing both parts by their greatest common factor gives the simplest form.

Answer

$0.08 = \frac{2}{25}$

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$75 %$

Multiply the numerator and denominator by $25$ : $\frac{3}{4} = \frac{75}{100} = 75 %$ . The whole remains unchanged throughout the conversion.

Keep practising

6 worksheet questions · 13 marks

Open worksheet 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.

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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 ↗

In this lesson

Understand the idea.

Percent means per hundred

Keep the whole consistent

See the method in action.

Use hundredths

Make hundredths.

Read the decimal.

Write the percentage.

Convert a small percentage

Write the percentage as hundredths.

Read the decimal places.

Simplify the fraction.

Try it yourself.

Check your understanding

Keep practising