Rounding and Significant Figures: Rules and Examples

To round, find the last digit you want to keep and look at the next digit: 5 or more, round up; less than 5, keep it. Decimal places count from the decimal point, while significant figures count from the first non-zero digit.

Rounding to decimal places

$3.14159$ to 2 decimal places: keep $3.14$, look at the next digit, $1$. It is less than 5, so the answer is $3.14$.

$2.678$ to 1 decimal place: the next digit is $7$, so round up to $2.7$.

Rounding to the nearest 10, 100 or 1000

$2749$ to the nearest 100: the hundreds digit is 7 and the next digit is 4, so round down to $2700$. Zeros hold the place value.

Rounding to significant figures

Start counting at the first non-zero digit.

$0.0045678$ to 3 s.f.: the first three significant digits are $4, 5, 6$, the next is $7$, so the answer is $0.00457$.

$48\,350$ to 2 s.f.: $48$, next digit $3$, so $48\,000$.

Counting significant figures

Halves

The common school rule rounds a 5 up: $2.5 \to 3$. Some systems use "round half to even" ($2.5 \to 2$) to avoid bias in large data sets.

Common mistakes

• Rounding in stages: $2.449 \to 2.45 \to 2.5$ is wrong; to 1 d.p. it is $2.4$.
• Dropping place-holder zeros: $2749$ to the nearest 100 is $2700$, not $27$.
• Counting leading zeros as significant.

Practice questions

1. Round $7.8263$ to 2 d.p.
2. Round $0.030719$ to 2 s.f.
3. How many s.f. in $40.20$?

Answers: 1) $7.83$ 2) $0.031$ 3) 4

Use the rounding calculator for any of these, count digits with the significant figures counter, and see scientific notation explained.

Frequently asked questions

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