Significant Figures Calculator
Count significant figures in any number or round a number to a specific number of sig figs. Enter any number to see which digits are significant and why.
How Significant Figures Calculator works
Rules for counting significant figures
All non-zero digits are significant. Zeros between non-zero digits are significant (e.g. 305 has 3 sig figs). Leading zeros are never significant (e.g. 0.0045 has 2 sig figs). Trailing zeros after a decimal point are significant (e.g. 2.50 has 3 sig figs). Trailing zeros in a whole number without a decimal point are ambiguous (e.g. 1500 could be 2, 3, or 4 sig figs depending on context).
Rounding to significant figures
To round to N significant figures: start from the first non-zero digit, count N digits, then round normally (5 or above rounds up, below 5 rounds down). For example, 0.004567 to 2 sig figs: the first significant digit is 4, counting two digits gives 45, rounding at the next digit (6 ≥ 5) gives 0.0046.
Why significant figures matter
Significant figures indicate the precision of a measurement. A length of 3.50 m (3 sig figs) is more precise than 3.5 m (2 sig figs) — the trailing zero tells you the measurement was taken to the nearest centimetre. When performing calculations with measured values, the result should have the same number of sig figs as the least precise input.
Sig figs in calculations
For multiplication and division, the result should have the same number of significant figures as the input with the fewest sig figs. For addition and subtraction, the result should have the same number of decimal places as the input with the fewest decimal places. These rules prevent overstating the precision of calculated results.
Frequently asked questions
How many significant figures does 0.0045 have?
0.0045 has 2 significant figures (4 and 5). The leading zeros (0.00) are not significant — they only indicate the position of the decimal point. If it were written as 0.00450, it would have 3 significant figures because the trailing zero after a decimal is significant.
Are trailing zeros significant?
It depends. Trailing zeros after a decimal point are always significant (e.g. 2.50 has 3 sig figs). Trailing zeros in a whole number without a decimal point are ambiguous: 1500 could have 2, 3, or 4 sig figs. To be clear, write 1500. (with a decimal point, 4 sig figs) or 1.5 × 10^3 (2 sig figs).
How do I round to 3 significant figures?
Find the first non-zero digit, count three digits from it, and round at the next digit. Examples: 45,678 → 45,700 (3 sig figs). 0.0034567 → 0.00346 (3 sig figs). 1,005 → 1,010 (3 sig figs, but this is ambiguous — better to write 1.01 × 10^3).
How many sig figs does 100 have?
This is ambiguous. 100 could have 1 sig fig (only the 1 is significant), 2 sig figs, or 3 sig figs. To clarify: 100. (with a decimal point) = 3 sig figs; 1.0 × 10^2 = 2 sig figs; 1 × 10^2 = 1 sig fig. In this calculator, enter the number as written to count based on the representation.
What is the difference between significant figures and decimal places?
Decimal places count digits after the decimal point. Significant figures count all meaningful digits regardless of the decimal. For example, 0.0045 has 4 decimal places but only 2 significant figures. 123.4 has 1 decimal place but 4 significant figures. Sig figs convey precision; decimal places convey resolution.
Why do scientists use significant figures?
Significant figures communicate the precision of a measurement. Every measurement has uncertainty — a ruler marked in mm gives 3 sig figs (e.g. 25.4 mm), not 5 (25.400 mm). Reporting the right number of sig figs prevents falsely implying that a result is more precise than the instruments allow.
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