Fractions, decimals & percentages
Comparing & ordering
You cannot compare a fraction with a decimal while they look different. Convert them all to one form first, then it is easy.
Convert before you compare
To compare a mixture of fractions, decimals and percentages, change them all into the SAME form. Decimals are usually easiest, because you can then compare column by column. 3/4 = 0.75, 70% = 0.7. Since 0.75 > 0.7, three quarters is bigger.
Comparing decimals column by column
Compare the whole numbers first. If they match, compare the tenths, then the hundredths. 0.2, 0.3, 2.3, 2.4, 3.2 in order: 0.2, 0.3, 2.3, 2.4, 3.2. Watch out: more digits does not mean a bigger number. 0.25 is smaller than 0.3, because 2 tenths is less than 3 tenths.
The comparison symbols
< means 'is less than' > means 'is greater than' = means 'is equal to' The wide end always faces the bigger number. 0.4 < 50% because 0.4 = 40% 1/4 = 25% because both are 0.25 0.9 = 90%
Spotting the odd one out
A useful check is to convert a whole group and see which one does not belong. 1/5, 20%, 0.2 and 2/10 all equal 0.2 — they are the same value in different clothes. Anything else in that list, such as 1/2, would be the odd one out.
Worked examples
Which is bigger, 3/4 or 70%?
- 3/4 = 0.75.
- 70% = 0.7.
- 0.75 is greater than 0.7.
Answer: 3/4 is bigger
Ordering 2.4, 0.3, 3.2, 2.3, 0.2
- Compare whole numbers first: 0, 0, 2, 2, 3.
- Then the tenths within each group.
Answer: 0.2, 0.3, 2.3, 2.4, 3.2
Fill in the symbol: 0.4 ▢ 50%
- Convert 0.4 to a percentage: 40%.
- 40% is less than 50%.
Answer: 0.4 < 50%
Fill in the symbol: 1/4 ▢ 25%
- 1/4 = 0.25.
- 25% = 0.25.
- They are the same value.
Answer: 1/4 = 25%
Ordering 70%, 3/4 and 0.71
- 70% = 0.7.
- 3/4 = 0.75.
- Now compare 0.7, 0.75 and 0.71.
Answer: 70%, 0.71, 3/4
Where you see this in real life
- Comparing two sale offers, one '30% off' and one 'a third off'.
- Deciding which test score is better: 17/20 or 82%.
- Ordering race times where some are written as 10.85 and others as 10.9.
Key words
- Equivalent
- Of equal value, written differently.
- Order
- Arrange from smallest to largest.
- Compare
- Decide which is bigger or smaller.
- Less than (<)
- The symbol meaning smaller than.
- Greater than (>)
- The symbol meaning bigger than.
- Tenths
- The first column after the decimal point.