Which digits count
Significant figures (s.f.) are the digits in a number that carry real information about its size and precision. Counting them correctly lets you round sensibly and report a measurement to a fair level of accuracy.
Key idea
All non-zero digits are significant. Zeros between non-zero digits are significant (3405 has 4 s.f.). Leading zeros are not significant (0.0058 has 2 s.f.). Trailing zeros after a decimal point are significant (6.020 has 4 s.f.).
Rounding to a given number of s.f.
To round, keep the required number of significant digits and look at the next digit. If it is 5 or more, round up; if it is 4 or less, round down. Then replace the remaining digits with zeros or drop them as needed to keep the number's size.
Worked example
Round 47.85 to 3 significant figures. The first three significant digits are 4, 7 and 8. The next digit is 5, so round the 8 up to 9. The answer is 47.9. If instead we rounded 25 830 to 2 s.f., we keep 2 and 5, the next digit is 8 (round up), giving 26 000.
Common slips
Keep the number roughly the same size after rounding — 25 830 to 2 s.f. is 26 000, not 26. With small decimals, leading zeros only hold place value; 0.004736 to 2 s.f. is 0.0047.
Remember
- Leading zeros never count; sandwiched zeros always count.
- Look only at the very next digit when deciding to round up.
- Do not change the size (place value) of the number.