Significant Figures Calculator Calculators

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Significant figures (sig figs) are the meaningful digits in a measurement — all certain digits plus the first uncertain digit. They communicate the precision of a measurement: a measurement of 12.34 cm has four significant figures, indicating the measurement is precise to the nearest 0.01 cm. Rules for significant figures govern how to report calculated results so that the answer doesn't imply more precision than the least-precise measurement used. Sig fig rules differ for addition/subtraction (based on decimal places) versus multiplication/division (based on significant figure count).

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Rules for Counting Significant Figures

  • All nonzero digits are significant: 4567 → 4 sig figs
  • Zeros between nonzero digits are significant: 4007 → 4 sig figs
  • Leading zeros are NOT significant: 0.0045 → 2 sig figs
  • Trailing zeros after a decimal point ARE significant: 3.400 → 4 sig figs
  • Trailing zeros without a decimal point are ambiguous: 1500 → 2, 3, or 4 sig figs (use scientific notation to clarify: 1.5 × 10³ = 2 sig figs; 1.500 × 10³ = 4 sig figs)

Sig Fig Rules for Calculations

Multiplication and division: Round the result to the same number of sig figs as the measurement with the fewest sig figs.
Example: 4.56 × 1.4 = 6.384 → round to 2 sig figs → 6.4

Addition and subtraction: Round the result to the same number of decimal places as the measurement with the fewest decimal places.
Example: 12.34 + 1.5 + 0.021 = 13.861 → round to 1 decimal place → 13.9

Rounding Rules

If the next digit is < 5: round down (truncate). If ≥ 5: round up. For the digit exactly 5 with nothing following: round to even (banker's rounding) to reduce bias — 2.5 → 2; 3.5 → 4.

Glossary

Significant Figures (Sig Figs)
The meaningful digits in a measurement: all certain digits plus the first uncertain digit; communicate precision; rules differ for multiplication/division vs. addition/subtraction.
Leading Zeros
Zeros to the left of the first nonzero digit (e.g., 0.0035); not significant; serve only as placeholders; the number of significant figures begins at the first nonzero digit.
Trailing Zeros
Zeros at the end of a number; significant only if a decimal point is present (3.400 = 4 sig figs); ambiguous without a decimal (3400 could be 2–4 sig figs); clarified by scientific notation.

Frequently Asked Questions

Significant figures are the meaningful digits in a number that reflect measurement precision. They matter because a calculated result cannot be more precise than the measurements used to obtain it. If you measure 12.3 cm and 1.4 cm and multiply them, the answer should have 2 sig figs (not 17.22 — that implies false precision). Reporting 17 cm correctly reflects that both measurements together give only 2 significant digits of reliable information. Sig figs communicate uncertainty honestly in scientific reporting.

Rules: (1) All nonzero digits are significant: 935 = 3 sig figs. (2) Zeros between nonzero digits are significant: 9035 = 4 sig figs. (3) Leading zeros (left of first nonzero digit) are NOT significant: 0.0035 = 2 sig figs. (4) Trailing zeros after a decimal point ARE significant: 2.500 = 4 sig figs. (5) Trailing zeros without a decimal are ambiguous: 2500 could be 2, 3, or 4 sig figs — use scientific notation (2.5 × 10³ = 2 sig figs) to be precise.

Multiplication/division: the answer has as many sig figs as the factor with the fewest sig figs. Example: 3.21 (3 sig figs) × 1.2 (2 sig figs) = 3.852 → report as 3.9 (2 sig figs). Addition/subtraction: the answer has as many decimal places as the addend with the fewest decimal places. Example: 123.4 + 5.67 + 0.023 = 129.093 → fewest decimal places = 1 (from 123.4) → report as 129.1.

Identify the digit at the target position; look at the next digit: if it's 0–4, truncate; if it's 5–9, round up the target digit by 1. Examples: round 3.567 to 3 sig figs → look at 4th digit (7 ≥ 5) → round up → 3.57. Round 0.004521 to 2 sig figs → significant digits start at 4; 3rd sig digit is 2 (< 5) → 0.0045. Round 1.2850 to 3 sig figs → 3rd sig digit is 8; next is 5 (followed by 0) → round to even → 1.28 or 1.29 depending on method used.