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 .
Significant figures 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.
Rounding to the wrong number of significant figures 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. (significant figures) instead of the correct .
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 calculation
Rounding intermediate values too early (or to too few figures) and then continuing makes the final answer drift, costing the final accuracy mark.
Give the answer to the accuracy the question asks for
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.
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.
Round 3.04752 to 2 decimal places.
Round to significant figures.
