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To round to significant figures, count from the first non-zero digit, then look at the next digit: if it is 5 or more, round up. 14 questions answered.
Rounding Numbers and Measures is part of Measures and accuracy in GCSE AQA Higher Maths.
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GCSE AQA Higher
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To round to significant figures, count from the first non-zero digit, then look at the next digit: if it is 5 or more, round up. 14 questions answered.
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Use this lesson to stay inside Measures and accuracy while connecting the detail back to the wider Number topic.
Read the core explanations from Rounding Numbers and Measures before testing yourself from memory.
A calculator gives you $\pi \approx 3.14159265...$, but a builder measuring a circular pipe does not need fifteen digits. Rounding lets you express a number at the right level of precision for the situation — and examiners test whether you can do this accurately and choose wisely.
There are two main methods: rounding to a given number of decimal places (d.p.) and rounding to a given number of significant figures (s.f.). Both follow the same core rule, but they count digits differently. Get the counting right and the rest follows.
Think of it like a queue: you count along the digits after the decimal point until you reach your target position, then you peek at the very next digit to decide whether to round up or stay put. That single peek digit is called the deciding digit.
Worked example: Rounding to Decimal Places
Round $7.3862$ to (a) 1 decimal place and (b) 2 decimal places.
Answer: (a) $7.4$ (b) $7.39$
Notice that in part (b) the 8 rounded up to 9 — it did not carry over and change the digit before it. That only happens if the target digit is 9 and rounds up to 10, which causes a carry. Watch for that in trickier numbers like $3.997$ rounded to 2 d.p., which gives $4.00$.
Significant figures work differently from decimal places because you count from the first non-zero digit, regardless of where the decimal point sits. This makes the method powerful for very large numbers (like $3{,}700{,}000$) and very small numbers (like $0.00042$) where decimal places would be impractical.
Worked example: Rounding to Significant Figures — Decimal
Round $0.004806$ to (a) 1 s.f. and (b) 3 s.f.
Answer: (a) $0.005$ (b) $0.00481$
Worked example: Rounding to Significant Figures — Large Number
Round $38{,}472$ to (a) 1 s.f. and (b) 3 s.f.
Answer: (a) $40{,}000$ (b) $38{,}500$
Rounding is not always about following an instruction — sometimes the question asks you to choose how precise to be. The rule of thumb: match the precision of your answer to the precision of the data given, or to the context of the problem.
Rounding questions often lead to common errors, particularly with decisions related to precision. Students must practices developing systematic approaches to rounding accurately. For example, applying the rounding rules in different contexts helps in understanding the implications of precision. Regular practice, alongside expectation settings on what acceptable rounding looks like, reduces errors significantly around GCSE exams.
Rounding to an appropriate degree of accuracy — whether by decimal places or significant figures — is a skill that runs through the entire GCSE course. Every time you calculate an answer and the question specifies a precision, these rules apply. Practise identifying the deciding digit quickly and the carry-propagation cases will stop catching you out.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
To round to significant figures, count from the first non-zero digit, then look at the next digit: if it is 5 or more, round up. For example, 0.004806 is 0.005 to 1 s.f. and 0.00481 to 3 s.f., and 38,472 is 38,500 to 3 s.f.
Decimal places (d.p.) are the count of digits after the decimal point. To round to n decimal places, look at the next digit after the nth one: if it is 5 or more, round up; if it is 4 or less, leave the nth digit unchanged.
To round to n decimal places, look at the deciding digit, the next digit after the nth decimal place: if it is 5 or more round up, and if it is 4 or less leave the digit unchanged. For example, 7.3862 is 7.4 to 1 d.p. and 7.39 to 2 d.p.
An appropriate degree of accuracy matches the precision of the data given or the context. Money is rounded to 2 d.p. (the nearest penny), large populations or distances to 1–3 s.f., and an exam answer must use exactly the degree of accuracy stated.
Decimal places count digits after the decimal point, while significant figures count from the first non-zero digit, regardless of where the decimal point sits. Significant figures are more useful for very large numbers like 3,700,000 and very small numbers like 0.00042.
Leading zeros in decimals, and trailing zeros in whole numbers used only to position the decimal point, are not significant. A zero between two non-zero digits is significant, so in 0.004806 the zero between the 8 and the 6 is the third significant figure.
3.997 rounded to 2 decimal places is 4.00. The target digit 9 rounds up to 10, which causes a carry into the digits before it, giving 4.00.
7.3862 to 1 decimal place is 7.4. The digit in the first decimal place is 3, and the deciding digit after it is 8, which is 5 or more, so the 3 rounds up to 4; to 2 decimal places it is 7.39.
0.004806 to 1 significant figure is 0.005. The first non-zero digit is 4 and the deciding digit is 8, so it rounds up to 5, and the placeholder zeros are kept; to 3 significant figures it is 0.00481.
38,472 to 1 significant figure is 40,000. The first digit is 3 and the deciding digit is 8, so 3 rounds up to 4 and zeros replace the other digits; to 3 significant figures it is 38,500.
The deciding digit is the digit just after the target position, which decides whether to round up or stay put. If it is 5 or more, the target digit rounds up; if it is 4 or less, the target digit is left unchanged.
Money is rounded to 2 decimal places, which is the nearest penny, for example £3.47. The same 5-or-more rule applies to the digit in the third decimal place.
Large populations or distances are usually rounded to 1–3 significant figures to avoid false precision, for example 4,200,000 people to 2 significant figures. Zeros replace the remaining digits so the number stays the right size.
When a 9 rounds up it becomes 10, which causes a carry into the digit before it. For example, 3.997 rounded to 2 decimal places gives 4.00, because the 9 in the second decimal place rounds up and carries.