Significant figures: how to round and count them

Q: Is 0 a significant figure in 105?

Yes. A zero between two non-zero digits always counts, so 105 has 3 significant figures.

Q: How many significant figures should I give in an exam answer?

Follow the question if it says. If it doesn't and the answer isn't exact, 3 significant figures is the usual choice in GCSE Maths. Keep full accuracy in your calculator until the end and round only the final answer.

Q: Do zeros count as significant figures?

Zeros at the start (0.004) never count. Zeros between other digits (507) always count. Zeros at the end after a decimal point (2.50) count, and zeros at the end of a whole number (4,000) may or may not, depending on how it was rounded.

Q: How do you round to 1 significant figure?

Keep only the first non-zero digit, round it using the digit after it, and fill the rest with zeros to keep the place value. 0.0368 becomes 0.04 and 6,520 becomes 7,000.

Q: Why use significant figures instead of decimal places?

Significant figures show precision for numbers of any size. 0.000123 to 2 decimal places is 0.00, which loses everything, but to 2 significant figures it's 0.00012.

TutorAura guide · Updated 25 October 2026

Significant figures (s.f.) are the digits that carry meaning in a number, counted from the first non-zero digit. To round to a number of significant figures, count that many digits from the first non-zero digit, look at the next digit, and round up if it's 5 or more. Then fill with zeros to keep the place value:

$3{,}846$ to 2 s.f. $= 3{,}800$
$0.004572$ to 2 s.f. $= 0.0046$

Key takeaways

Start counting at the first non-zero digit.
Leading zeros never count; zeros between digits always count.
Keep place value: fill with zeros in big numbers.
Round to 1 s.f. to estimate an answer.

Which zeros count?

Number	Significant figures	Why
0.0045	2	Leading zeros don't count
50.07	4	Zeros between non-zero digits count
0.0300	3	Trailing zeros after a decimal point count
4,000	1 to 4	Ambiguous: depends on how it was rounded

Worked examples

$4.0596$ to 3 s.f.: digits 4, 0, 5; next digit 9, so round up: 4.06.
$239{,}500$ to 3 s.f.: digits 2, 3, 9; next digit 5, so round up: 240,000.
$6.997$ to 3 s.f.: rounding up carries through: 7.00 (keep the zeros to show 3 s.f.).
$0.07068$ to 2 s.f.: first non-zero digit is 7; digits 7, 0; next digit 6: 0.071.

Try your own with the rounding calculator.

Significant figures vs decimal places

Decimal places count from the decimal point; significant figures count from the first non-zero digit. $0.004572$ to 2 decimal places is $0.00$ , but to 2 significant figures it's $0.0046$ . Significant figures suit numbers of any size, which is why science uses them.

Estimating

Round every number to 1 s.f., then calculate:

\frac{48.7 \times 3.1}{0.52} \approx \frac{50 \times 3}{0.5} = 300

Show the rounded numbers in an exam: the method mark is for them. See non-calculator tips.

Error intervals

If a number has been rounded, its true value lies in a range. Halve the unit you rounded to and go either side:

$x = 7.4$ to 1 d.p.: $7.35 \le x < 7.45$
$y = 3{,}800$ to 2 s.f. (nearest 100): $3{,}750 \le y < 3{,}850$

The lower bound uses $\le$ and the upper bound uses $<$ , because 7.45 would round up to 7.5.

Common mistakes

Counting leading zeros as significant.
Dropping place value: $3{,}846$ to 2 s.f. is $3{,}800$ , not 38.
Dropping trailing zeros that matter: $6.997$ to 3 s.f. is $7.00$ , not 7.
Using $\le$ for both ends of an error interval.

Practice

Round 6,482 to 2 significant figures.
Round 0.03049 to 3 significant figures.
Round 7.0451 to 3 significant figures.
Estimate $31.8 \times 0.49$ by rounding to 1 significant figure.
$m = 12$ to 2 s.f. Write the error interval for $m$ .

Answers: 6,500; 0.0305; 7.05; $30 \times 0.5 = 15$ ; $11.5 \le m < 12.5$ .

Frequently asked questions

Is 0 a significant figure in 105?

Yes. A zero between two non-zero digits always counts, so 105 has 3 significant figures.

How many significant figures should I give in an exam answer?

Follow the question if it says. If it doesn't and the answer isn't exact, 3 significant figures is the usual choice in GCSE Maths. Keep full accuracy in your calculator until the end and round only the final answer.

Do zeros count as significant figures?

Zeros at the start (0.004) never count. Zeros between other digits (507) always count. Zeros at the end after a decimal point (2.50) count, and zeros at the end of a whole number (4,000) may or may not, depending on how it was rounded.

How do you round to 1 significant figure?

Keep only the first non-zero digit, round it using the digit after it, and fill the rest with zeros to keep the place value. 0.0368 becomes 0.04 and 6,520 becomes 7,000.

Why use significant figures instead of decimal places?

Significant figures show precision for numbers of any size. 0.000123 to 2 decimal places is 0.00, which loses everything, but to 2 significant figures it's 0.00012.

Sources

National curriculum in England: mathematics programmes of study. Department for Education.
Common Core State Standards for Mathematics. Common Core State Standards Initiative.
Mathematics GCSE subject content and assessment objectives. Department for Education.

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