Rounding calculator: significant figures and decimal places

The first significant figure is the first non-zero digit. Count from there, then look at the next digit: 5 or more rounds up.

Zeros at the start of a small number (0.00…) are not significant; zeros between other digits are. Large numbers keep their size with zeros: 38,472 to 2 s.f. is 38,000, not 38.

In every row, the digit straight after the last one you keep decides. Large numbers keep their size with zeros (6482 becomes 6000, not 6), and digits after the decimal point are simply dropped.

Count digits after the decimal point. To round 3.14159 to 3 d.p., look at the 4th decimal digit (5): round up, giving 3.142. Keep trailing zeros that show the accuracy: 2.5 to 2 d.p. is 2.50.

Rounding every number to 1 s.f. is a quick way to estimate and check answers: $\dfrac{38.7 \times 5.12}{0.48} \approx \dfrac{40 \times 5}{0.5} = 400$. Estimation questions are common in non-calculator papers; see our significant figures guide.

• Counting leading zeros as significant figures.
• Rounding in stages (2.346 → 2.35 → 2.4) instead of once (2.346 → 2.3 to 1 d.p.).
• Dropping place value: 38,472 to 2 s.f. is 38,000, not 38.

When a measurement is rounded, the true value lies in a range. A length of 7.4 cm to 1 decimal place could be anything from 7.35 cm (the lower bound) up to, but not including, 7.45 cm (the upper bound): half a unit either side. GCSE Higher questions use bounds to find the largest or smallest possible result of a calculation, for example the maximum area of a rectangle measured to the nearest centimetre.

• Money is usually given to 2 decimal places: £3.456 → £3.46.
• Lengths and masses often use the same accuracy as the question or a sensible number of significant figures.
• If a question doesn't say, 3 significant figures is a safe default in GCSE maths, but give the full calculator value in your working first.