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. (decimal places) 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. (significant figures) it is . Leading zeros are place-holders and never count.
Estimate by rounding each value to 1 s.f.
To estimate a calculation, round every number to 1 s.f. (significant figure) first, then work it out. E.g. estimates as .
Drawn from real examiner reports.
Leading zeros counted as significant
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. (significant figures) instead of the correct .
A recurring small-number rounding error; on Nov 2024 Paper 1H examiners stressed giving answers "to the degree of accuracy stated in the question" (e.g. rounding 12.750... to 3 s.f.).
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.
Premature rounding in a multi-step sum
Rounding intermediate values too early (or to too few figures) and then continuing makes the final answer drift, costing the final accuracy mark.
On Nov 2024 Paper 2H examiners reported that "premature rounding cost some students the final accuracy mark" and advised keeping plenty of decimal places or using the calculator memory.
Mixing up the d.p. and s.f. rules
Decimal places count from the point; significant figures count from the first non-zero digit. So is to 3 d.p. but to 2 s.f. — reading "d.p." as "s.f." (or the reverse) applies the wrong rule and gives a different answer.
Dropping place-holder zeros in a large number
Rounding a large number to s.f., fill the gap back to the decimal point with zeros: to 2 s.f. is , not . The place-holder zeros keep the significant digits in the right columns.
Round at the end to the stated accuracy
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.
Use an estimate to sanity-check the size
After a calculator answer, round to 1 s.f. and redo it roughly: the estimate should match the SIZE. If the calculator gives and your estimate is about it is sensible; an answer of or signals a keying error.
Keep full precision, round only at the end
Carry the full unrounded value (or the calculator memory) through every step, and round only the final answer. This avoids the premature-rounding drift that costs the last accuracy mark.
Small divisors make the answer bigger
Dividing by a small decimal makes the answer BIGGER: is the same as . In an estimate, expect a large result when you divide by a number below — do not "correct" it downwards.
Decimal places count digits after the decimal point. To round to d.p. (decimal places), 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.
Where do you start counting significant figures?
Round to significant figures.
