Estimate by rounding each value to 1 s.f.
To estimate a calculation, round every number to 1 significant figure first, then work it out. E.g. estimates as .
Decimal places count digits AFTER the point
To round to decimal places, look at the digit in the th place after the point: or more rounds up, or less rounds down. E.g. to 2 d.p. is .
s.f. start at the first non-zero digit
Counting significant figures starts at the first non-zero digit, NOT at the decimal point. So in the first significant figure is the ; to 2 s.f. it is . Leading zeros are place-holders and never count.
Drawn from real examiner reports.
Wrong s.f. with leading zeros
With small numbers like , students start counting at the wrong place — treating the leading zeros as significant — so they give or to 2 s.f. instead of the correct .
A recurring small-number rounding error; on a recent higher-tier paper examiners stressed giving answers "to the degree of accuracy stated in the question" (e.g. rounding 12.750... to 3 s.f.).
Premature rounding mid-calculation
Rounding intermediate values too early (or to too few figures) and then continuing makes the final answer drift, costing the final accuracy mark.
A commonly reported examiner note records examiners reported that "premature rounding cost some students the final accuracy mark" and advised keeping plenty of decimal places or using the calculator memory.
Not rounding BEFORE estimating
Students work the calculation out exactly (or on a calculator) and only round at the very end. An estimate requires rounding each value to 1 s.f. FIRST — otherwise it is not an estimate and earns no method marks.
Confusing decimal places with s.f.
Decimal places count from the point; significant figures count from the first non-zero digit. is to 3 d.p. but to 2 s.f. — different rules, different answers.
Forgetting to keep a trailing zero
Rounding to 2 d.p. gives — the rounds up and carries, and you keep the trailing zero to show the accuracy. Writing drops a required figure.
Answer to the accuracy asked
If a question says "to 3 significant figures", round AT THE END to exactly that — do not leave the long unrounded value, and do not over-round earlier steps.
Round to 1 s.f. to sanity-check
Use a 1 s.f. estimate to check a calculator answer is the right size: . A result of or flags a keying error.
Keep full accuracy until the last step
Carry every intermediate value to plenty of figures (or use the calculator memory), and round only once at the very end to the accuracy asked. This avoids the drift that premature rounding causes.
Decimal places count digits after the decimal point. To round to d.p., look at the next digit (the th):
Watch for a carry: to 2 d.p. is (the rounds up and carries), and you keep the trailing zero to show the accuracy.
Round 3.04752 to 2 decimal places.
Round to decimal places.
