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3.3b · Estimation · Sub-skill
Rounding to a sensible degree of accuracy — decimal places, significant figures, and choosing the right precision for the context.
Build it up, step by step
Click each step below to reveal it — work through them in order the first time round.
To round to a given number of decimal places (d.p.), look at the digit after the last one you're keeping. If it's 5 or more, round up; otherwise round down. E.g. 3.647 rounded to 1 d.p. is 3.6 (the next digit, 4, is less than 5).
The first significant figure is the first non-zero digit; count significant figures (s.f.) from there, including any zeros in between. E.g. 0.004072 to 2 s.f. is 0.0041. Significant figures are especially useful for very large or very small numbers.
The context of a question tells you how precise your answer should be. Money is usually rounded to 2 decimal places (the nearest penny); a population might be rounded to 3 significant figures. Over-rounding loses useful information; under-rounding implies false precision.
Every time you round a number, you introduce a small error. If a length is given as 12 cm to the nearest cm, the true value could be anywhere from 11.5 cm up to (but not including) 12.5 cm — these are the lower and upper bounds. Rounding error matters especially when you do further calculations with already-rounded figures.
Round 58,439 to (a) the nearest 1000, (b) 2 significant figures.
(a) The digit after the thousands place is 4 (hundreds digit), so round down: 58,000.
(b) The first two significant figures are 5 and 8; the next digit is 4, so round down: 58,000.
Test yourself
A stadium's attendance is recorded as 24,850, correct to the nearest 10.
(a) Write down the upper and lower bounds for the actual attendance.
(b) A newspaper reports the attendance as ‘about 25,000, to 2 significant figures.’ Explain whether this is an appropriate degree of accuracy for a newspaper headline. [4 marks]
(a) Lower bound = 24,845, Upper bound = 24,855 (the true value could be anywhere from 24,845 up to but not including 24,855).
(b) Yes, this is appropriate — for a general newspaper headline, readers don't need the exact attendance to the nearest person; rounding to 2 significant figures gives a clear, easy-to-read sense of scale, which is all that's needed in this context.
Practice
Five short questions on rounding. Work through them, then reveal the mark scheme to check.