Rounding
Rounding means writing a number to a stated level of accuracy, such as the nearest 10, a number of decimal places, or a number of significant figures, while keeping it as close as possible to the original value. It is used throughout GCSE Maths to estimate calculations and to give sensible final answers on calculator questions.
Method
- Identify the place value column you are rounding to, and look at the digit immediately to its right, the decider digit.
- If the decider digit is 5 or more, round the previous digit up by 1; if it is 4 or less, leave the previous digit unchanged.
- For rounding to a whole number or the nearest 10, 100 or 1000, replace all digits after the rounding point with zeros up to the decimal point.
- For decimal places, count that many digits after the decimal point and remove everything after, applying the rounding rule.
- For significant figures, count from the first non-zero digit, ignoring leading zeros in decimals, keeping placeholder zeros where needed to preserve the number's size.
- For estimation questions, round every number in the calculation to 1 significant figure first, then calculate with the rounded values.
Worked example
Round 3.0847 to 2 decimal places, then round 68,254 to 2 significant figures.
- For 3.0847 to 2 decimal places, look at the 3rd decimal digit, 4; since 4 is less than 5, round down.
- 3.0847 rounds to 3.08.
- For 68,254 to 2 significant figures, the first two significant figures are 6 and 8; the next digit is 2.
- Since 2 is less than 5, round down, keeping the first two figures and replacing the rest with zeros: 68,000.
- Final answer: 3.08 and 68,000.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
The number 7,382 people attended a festival. (a) Round 7,382 to the nearest 100. (1) (b) Round 7,382 to the nearest 1000. (1)
This question is about rounding to significant figures. (a) Round 528,471 to 3 significant figures. (2) (b) A company's annual revenue was 3,762,900 pounds. Round the revenue to 1 significant figure. (1)
This question is about rounding to significant figures and estimating. (a) Circle the number below that rounds to 7.0 when rounded to 2 significant figures. A) 6.94 B) 6.951 C) 7.06 D) 7.15 (1) (b) Amir buys 28 festival tickets at 22.75 pounds each. Estimate the total cost by rounding each number to 1 significant figure. (3)
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