To round, look at the digit just after the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down. This works for rounding to the nearest 10, 100 or 1000 and for rounding to a number of decimal places. Rounding each number in a calculation to 1 significant figure gives a quick estimate.
Rounding rules
- Look at the next digit after the place you are rounding to
- 5 or more: round up; 4 or less: round down
- Keep the place value: 26 482 to the nearest 1000 is 26 000, not 26
- For decimal places, keep the required number of digits after the point
Rounding to the nearest 10, 100 or 1000
Find the digit in the place you are rounding to, then look at the digit after it. For 3847 to the nearest 100, the hundreds digit is 8 and the next digit is 4, so round down to 3800. Fill the remaining places with zeros so that the number keeps its size.
Rounding to decimal places
To round to 2 decimal places, keep two digits after the point and look at the third. 3.847 has a third decimal digit of 7, so round up to 3.85. Keep any final zeros that are needed: 2.596 to 2 decimal places is 2.60, not 2.6.
Rounding up when the digit is 9
If the digit being rounded up is a 9, it becomes 0 and the next digit to the left increases: 4.97 to 1 decimal place is 5.0, and 1996 to the nearest 10 is 2000.
Rounding money and measurements
Money is normally rounded to 2 decimal places, the nearest penny. Answers in context should be rounded sensibly, but sometimes the context decides the direction: if each minibus seats 16 and 50 students travel, you need 4 minibuses, not 3.
Using rounding to estimate
Rounding every number to 1 significant figure makes a calculation easy to do mentally: 38 × 21 ≈ 40 × 20 = 800. An estimate is a useful check on a calculator answer and is often asked for directly on non-calculator papers.
Worked examples
Example 1. Round 26 482 to the nearest 1000.
- The thousands digit is 6; the next digit, the hundreds, is 4.
- 4 means round down.
Answer: 26 000.
Example 2. Round 5.768 to 1 decimal place.
- Keep one decimal digit, 7, and look at the next digit, 6.
- 6 means round up.
Answer: 5.8.
Example 3. Round 2.596 to 2 decimal places.
- The third decimal digit is 6, so round up.
- 2.59 becomes 2.60, keeping the final zero.
Answer: 2.60.
Example 4. Round 0.0473 to 2 decimal places.
- Keep two decimal places: 0.04. The next digit is 7.
- Round up.
Answer: 0.05.
Example 5. 50 students go on a trip. Each minibus carries 16 students. How many minibuses are needed?
- 50 ÷ 16 = 3.125.
- 3 minibuses carry only 48 students, so round up.
Answer: 4 minibuses.
Common mistakes
- Dropping the zeros. 26 482 to the nearest 1000 is 26 000, not 26.
- Looking at the wrong digit. Look at the digit immediately after the place you are rounding to.
- Losing a needed final zero. 2.596 to 2 decimal places is 2.60.
- Rounding in stages. Round the original number once; do not round 3.847 to 3.85 and then to 3.9.
- Rounding down in context when you must round up. You need enough minibuses for everyone.
How rounding is examined
Rounding is a basic Foundation skill in the 1MA1 and 4MA1 specifications, and accurate rounding is needed for final answers on every paper. Questions ask you to:
- round to the nearest 10, 100 or 1000
- round to a given number of decimal places
- round sensibly in a context such as money or transport
- estimate a calculation by rounding
Practise with the rounding and estimation worksheet, which includes answers, and the number revision engine.
Next, see significant figures and truncation and estimating calculations. Rounding also leads to error intervals.
Frequently asked questions
What is the rule for rounding?
Look at the next digit. If it is 5 or more, round up; if it is 4 or less, round down.
How do you round to 2 decimal places?
Keep two digits after the decimal point, then look at the third digit to decide whether to round up.
What is 3.95 to 1 decimal place?
4.0. The 9 rounds up, which carries into the units.