Round to a stated precision
Decimal places are counted from the decimal point, while significant figures are counted from the first non-zero digit. In either method, the next digit determines whether the last kept digit changes
- Read the requested precision Check whether the instruction asks for decimal places or significant figures \(\displaystyle 2\text{ d.p.}\ne2\text{ s.f.}\)
- Count decimal places For decimal places, count digits to the right of the decimal point \(\displaystyle 18.374\to18.37\text{ (2 d.p.)}\)
- Count significant figures For significant figures, start at the first non-zero digit and count from there \(\displaystyle 0.004768\to0.0048\text{ (2 s.f.)}\)
- Use the next digit A next digit from 5 to 9 rounds the last kept digit up; a next digit from 0 to 4 leaves it unchanged \(\displaystyle 7.286\to7.29\text{ (2 d.p.)}\)
- Show precision in scientific notation A carry can increase the exponent. Keep decimal zeros in the coefficient to state significant figures. This result is rounded to three significant figures \(\displaystyle 9.9962\approx1.00\times10^1\)
Worked example
An instrument records a coating thickness of 0.006482 m. State the thickness to 3 significant figures
- \(\displaystyle 0.006482=6.482\times10^{-3}\)The first three significant digits are 6, 4 and 8, and the next digit is 2
- \(\displaystyle 2<5\)Because the deciding digit is less than 5, the target digit stays unchanged
- \(\displaystyle 6.482\to6.48\)Keep the first three significant digits without increasing the last one
- \(\displaystyle 0.006482\text{ m}\approx0.00648\text{ m}\)The thickness to 3 significant figures is 0.00648 m
Common mistakes
Difficulty levels
Questions about this topic
What is the difference between decimal places and significant figures?+
Decimal places count digits after the decimal point. Significant figures start at the first non-zero digit and count digits from there
Which digit decides a rounding step?+
The first digit after the last place or significant figure being kept decides the step. Digits 5 to 9 round up, while digits 0 to 4 leave the kept digit unchanged
Do leading zeros count as significant figures?+
No. Leading zeros show the position of the decimal point, but they do not record measured precision
Does finer resolution guarantee accuracy?+
No. Resolution is the smallest displayed or marked change. Accuracy also depends on calibration and measurement conditions. Use the stated uncertainty or accuracy specification when choosing an instrument
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 6: Indices and surds