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Decimals and percentages are closely linked to fractions. On the SET 11+ maths papers, you need to convert between all three forms, carry out calculations with decimals, and solve percentage problems. This lesson covers the key skills with plenty of worked examples.
A decimal number uses a decimal point to separate the whole-number part from the fractional part.
| Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 3 | . | 4 | 7 | 5 |
The number 3.475 means 3 + 4/10 + 7/100 + 5/1000.
Line up the decimal points, fill in any missing zeros, and add or subtract as normal.
Calculate 14.6 - 7.85.
Write as 14.60 - 7.85.
Answer: 6.75
Method: Ignore the decimal points, multiply the whole numbers, then put the decimal point back in.
Calculate 3.4 × 0.6.
Multiply 34 × 6 = 204. Count the total decimal places in the question: 1 + 1 = 2. Place the decimal point 2 places from the right.
Answer: 2.04
To divide by a decimal, multiply both numbers by 10 (or 100) to make the divisor a whole number, then divide as normal.
Calculate 7.2 ÷ 0.4.
Multiply both by 10: 72 ÷ 4 = 18.
You must know these key equivalents:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333... | 33.3...% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
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