Decimals and percentages
Decimals and percentages are fractions in disguise. Year 6 pupils need to move between all three forms, calculate with decimals in written methods, and find percentages of amounts using a few building blocks.
Decimal place value
The places to the right of the decimal point are tenths, hundredths and thousandths. In 3.457, the 4 is worth 4 tenths, the 5 is 5 hundredths and the 7 is 7 thousandths. Year 6 pupils read, write, order and compare numbers with up to three decimal places.
- 0.3 is bigger than 0.250.30 compared with 0.25: 30 hundredths is more than 25.
- 0.25 is bigger than 0.3 because it's longer“Longer is larger” only works for whole numbers.
That misconception is the most common one with decimals. Adding zeros so both numbers have the same number of decimal places (0.30 and 0.25) makes the comparison obvious. Reading 0.15 as “one tenth and five hundredths” rather than “point fifteen” helps too.
Calculating with decimals
Written methods for decimals work exactly as for whole numbers, provided the place values stay lined up. In addition and subtraction, that means lining up the decimal points. In multiplication by a single digit, multiply as normal and place the decimal point in the answer using an estimate: 3.6 × 7 is about 4 × 7 = 28, so the answer 25.2 is sensible.
- 12.5 − 3.75 = 12.50 − 3.75 = 8.75Fill the empty place with a zero.
- 3.6 × 7 = 25.2Estimate: about 28.
Percentages
A percentage is a number of parts per hundred: 35% means 35 out of 100. Year 6 pupils find percentages of amounts and solve problems involving percentages. The most flexible method is building blocks:
- 50%: halve.
- 10%: divide by 10.
- 5%: halve 10%.
- 1%: divide by 100.
- 15% of 360 = 10% (36) + 5% (18) = 54Combine building blocks.
- 5% of 360 = 360 ÷ 5 = 72Dividing by 5 finds 20%, not 5%.
Other percentages are combinations: 35% is 25% + 10%, or 50% − 15%. Children who know the building blocks can find almost any percentage mentally.
Fractions, decimals and percentages
Pupils should recognise the common equivalences instantly and convert between the three forms:
| Fraction | Decimal | Percentage |
|---|---|---|
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ¾ | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
| ⅕ | 0.2 | 20% |
| 1/100 | 0.01 | 1% |
For any fraction with a denominator that is a factor of 100, convert it to hundredths: 7/20 = 35/100 = 0.35 = 35%.
In the SATs
The arithmetic paper includes decimal addition, subtraction and multiplication, and percentages of amounts (such as 15% of 360). The reasoning papers test ordering decimals, placing them on number lines, converting between fractions, decimals and percentages, and percentage problems set in shopping or survey contexts.
Common mistakes
- Thinking a decimal with more digits is larger.
- Misaligning decimal points in column calculations.
- Dividing by 5 to find 5%, or by 20 to find 20%.
- Writing 0.5 as 5% instead of 50%.
- Placing the decimal point without estimating.
Teaching ideas
Place value charts with decimals
Extend the place value chart to thousandths. Pupils make numbers with digit cards and compare them column by column, starting from the left.
Percentage building blocks
Give a number such as 240 and ask pupils to find 50%, 10%, 5% and 1%. Then use only those to find 15%, 35%, 60% and 99%.
Matching cards
A set of cards with fractions, decimals and percentages to match in threes. Include a few that don't have a match, to stop guessing.
Shopping problems
Use real sale prices: 20% off £45, 15% off £120. Children calculate the discount and the new price. Money gives decimals a meaning children understand.
Try it: five quick questions
SATs-style questions to use as a starter or a quick check. Tap to see each answer.
Order from smallest: 0.6, 0.06, 0.66, 0.606
Show answer
0.06, 0.6, 0.606, 0.66
Calculate 14.3 − 6.85.
Show answer
7.45
Find 35% of 80.
Show answer
28
Write 3/20 as a percentage.
Show answer
15%
A coat costs £60. It's reduced by 25%. What's the new price?
Show answer
£45
Free worksheets for this topic
Printable A4 PDFs with answers. Free to use in class or at home.
