Decimals and percentages

The idea

A percentage is a fraction out of 100: 35% means 35/100. Decimals and percentages are the same idea in different clothes — 0.6 = 60/100 = 60%, and 0.05 = 5%.

To find a percentage of an amount, build it from friendly chunks. Find 10% by dividing by 10, halve that for 5%, and find 1% by dividing by 100. Then combine: 35% = 30% + 5%, so find 10%, triple it, add 5%.

When adding or subtracting decimals, line up the decimal points so tenths sit under tenths and hundredths under hundredths — this matters far more than lining up the ends of the numbers.

Worked example

Find 35% of 240.

1. Find 10% of 240: 240 ÷ 10 = 24.
2. 30% is three lots of 10%: 3 × 24 = 72.
3. 5% is half of 10%: 24 ÷ 2 = 12.
4. Add the chunks: 72 + 12 = 84.

Answer: 84

Watch out

• Finding 10% correctly but then not knowing how to build other percentages from it.
• Thinking 0.6 is 6% — it is 60%, because 0.6 = 60/100.
• Adding decimals without lining up the decimal points (2.5 + 0.75 is 3.25, not 2.80).