The rules, with examples
- Non-zero digits always count. 285 has 3.
- Zeros between non-zero digits count. 2005 has 4.
- Leading zeros never count. They only place the decimal point. 0.0042 has 2.
- Trailing zeros count if there's a decimal point. 2.500 has 4, and 250. has 3.
- Trailing zeros without a decimal point are unclear. 2500 could have 2, 3 or 4. Write it as 2.5 × 10³ (2) or 2.50 × 10³ (3) to be exact. NCERT counts them as not significant.
- Exact numbers have unlimited significant figures: 12 eggs in a dozen, or the 2 in 2πr.
In calculations
- Multiplying or dividing: keep as many significant figures as the least precise number. 2.5 × 3.42 = 8.55, which rounds to 8.6.
- Adding or subtracting: keep as many decimal places as the number with the fewest. 12.11 + 18.0 = 30.11, which rounds to 30.1.
Related: dimensional formulas for the Units and Measurement chapter.
Questions students ask
How many significant figures are in 0.0050?
2. The leading zeros don't count, but the trailing zero after 5 does, because there's a decimal point.
How many significant figures are in 100?
1 by the usual NCERT rule, since trailing zeros without a decimal point aren't counted. Written as 100. or 1.00 × 10², it has 3.
How many significant figures does 6.022 × 10²³ have?
4. The power of ten never affects the count.
How do you round 2.745 to 3 significant figures?
2.74 by the round-half-to-even rule NCERT uses, though many teachers accept 2.75. Check what your board expects.