Rounding Decimals
Every question with a fully worked solution.
- Rounding Decimals - Video - Rounding decimals Watch
Theory
Rounding a decimal gives a simpler number that is close to it. Keep the number of decimal places you need, and let the next digit decide: \(5\) or more rounds up, less than \(5\) rounds down. This Year 7 maths page shows how to round to one, two or three decimal places, how to carry when rounding up a \(9\), and when rounding makes sense.
Sometimes we need fewer decimal places than we calculate. Removing the extra places, and adjusting the last one we keep, is called rounding.
Rounding to \(1\) decimal place is rounding to the nearest tenth; \(2\) decimal places is the nearest hundredth; \(3\) decimal places is the nearest thousandth.
The deciding digit is the first digit after the places you keep. If it is 5 or more, round up: add \(1\) to the last digit you keep. If it is less than 5, round down: the kept digits stay the same.
The sign \(\approx\) means is approximately equal to: \(5.2683 \approx 5.27\). The two numbers are not equal, so do not write \(=\).
For example, \(10.921421\) is closer to \(10.921\) than to \(10.922\), and \(22.846901\) is closer to \(22.847\) than to \(22.846\).
How many places to keep:
| Round to the nearest | Places kept | Example |
|---|---|---|
| whole number | 0 | \(12.7 \approx 13\) |
| tenth | 1 | \(4.83 \approx 4.8\) |
| hundredth or cent | 2 | \(\$6.378 \approx \$6.38\) |
| thousandth | 3 | \(1.2346 \approx 1.235\) |
How to round a decimal
- Keep the places you need and draw a line after them: \(5.26 \mid 83\).
- Look at the deciding digit, the first digit after the line.
- 5 or more: add \(1\) to the last kept digit. Less than 5: leave it.
- Drop every digit after the line and write the answer with \(\approx\).
Keep three places: \(3.463 \mid 812\). The deciding digit is \(8\), and \(8 \ge 5\), so round up.
| \(3.463 + 0.001\) | \(=\) | \(3.464\) |
\(3.463812 \approx 3.464\)
Keep two places: \(5.71 \mid 4239\). The deciding digit is \(4\), and \(4 < 5\), so round down.
\(5.714239 \approx 5.71\)
(i) \(1\) decimal place
(ii) \(2\) decimal places
(iii) the nearest whole number
(i) \(15.3 \mid 862\): \(8 \ge 5\), round up.
(ii) \(15.38 \mid 62\): \(6 \ge 5\), round up.
(iii) \(15 \mid .3862\): \(3 < 5\), round down.
(i) \(15.4\)
(ii) \(15.39\)
(iii) \(15\)
(ii) Round \(0.0548\) to \(3\) decimal places.
| \(7.89 + 0.01\) | \(=\) | \(7.90\) |
| \(0.054 + 0.001\) | \(=\) | \(0.055\) |
(i) \(9\) hundredths becomes \(10\) hundredths and carries: \(7.896 \approx 7.90\).
(ii) Zeros after the point count as places: \(0.0548 \approx 0.055\).
\(5 \div 7 = 0.714285\ldots\) One centimetre is \(0.01\) m, so round to \(2\) decimal places: \(0.71 \mid 4285\ldots\), and \(4 < 5\).
Each piece is about \(0.71\) m (\(71\) cm). Check: \(7 \times 0.71 = 4.97\), close to \(5\).
Halfway between \(12.3\) and \(12.4\) is \(12.35\), which rounds up to \(12.4\). Halfway between \(12.4\) and \(12.5\) is \(12.45\), which rounds up to \(12.5\).
Only times from \(12.35\) to \(12.44\) round to \(12.4\): it could be \(12.35\) or \(12.41\).
Common pitfalls
Frequently asked questions
How do you round to 2 decimal places?
Keep two places, then look at the third. \(5.2683\): the deciding digit is \(8\), so \(5.27\).
What is the deciding digit?
The first digit after the places you keep. It decides whether to round up or down.
Does 5 round up or down?
Up. \(3.45\) rounds to \(3.5\) to one decimal place.
What happens when you round up a 9?
It becomes \(10\) and carries into the next place. \(7.896 \approx 7.90\).
What does the ≈ sign mean?
Is approximately equal to. Use it for rounded answers.