11+ Maths · Topic explained
How fractions, decimals and percentages link
Are 3/4, 0.75 and 75% the same thing?
The big idea
Fractions, decimals and percentages are three ways of writing the same amount.
Picture it
Think of £1 as 100 pennies: 25p is a quarter of a pound, £0.25, and 25% of it.
Key words
- per cent (%)
- Out of 100: 25% means 25 out of every 100.
- decimal
- A number with tenths and hundredths after a point: 0.25.
- convert
- Change from one way of writing to another.
Worked examples
- 1Warm-up
Write 1/2 as a decimal and a percentage
- 1/2 = 50/100
- = 0.5 = 50%
- 211+ standard
Write 3/5 as a percentage
- Make the bottom 100: × 20
- 3/5 = 60/100
- = 60%
- 311+ standard
Write 0.07 as a percentage and as a fraction
- 0.07 is 7 hundredths
- = 7% = 7/100
- 411+ standard
Put in order, smallest first: 0.3, 1/4, 28%
- Change them all to percentages
- 0.3 = 30%, 1/4 = 25%, 28%
- 1/4, 28%, 0.3
The common mistake
The mistake
0.07 = 70%.
Instead
0.07 = 7%; it's 0.7 that equals 70%.
Why: To turn a decimal into a percentage, × 100: 0.07 × 100 = 7.
Where it comes up in the 11+
Converting between the three, ordering mixed lists, and 'which is the biggest?' questions.
The video
Video coming soon
We're making a short video that explains how fractions, decimals and percentages link step by step. Until then, everything it covers is on this page.
Free printable
How fractions, decimals and percentages link worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
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Quick quiz
Have a go first, then tap to see the answer.
1. Write 1/5 as a percentage.
- 5%
- 15%
- 20%
- 50%
Show the answerHide the answer
20%
1/5 = 20/100 = 20%.
2. Write 0.4 as a fraction in its simplest form.
- 1/4
- 4/100
- 2/5
- 4/5
Show the answerHide the answer
2/5
0.4 = 4/10 = 2/5.
3. Which is the largest: 0.65, 2/3, 60% or 13/20?
- 0.65
- 2/3
- 60%
- 13/20
Show the answerHide the answer
2/3
2/3 ≈ 0.667; 13/20 = 0.65; 60% = 0.6.