Definition · Plain-language
Significant figures
Significant figures are the digits in a number that carry real information about the precision of a measurement, from the first non-zero digit to the last reliable one.
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Digits that carry meaning
Significant figures are the digits in a measured value that genuinely tell you something about its precision. They include every certain digit plus the first estimated one. If a ruler marked in millimetres gives a length of 24.3 millimetres, all three digits are significant: the 2 and 4 are certain and the 3 is the estimated final digit. Reporting the length as 24.300 would falsely claim precision to thousandths of a millimetre that the ruler cannot provide. Significant figures are therefore a compact way of communicating how good a measurement is.
The counting rules
A few rules settle which digits count. All non-zero digits are significant. Zeros between non-zero digits are significant, so 1,002 has four. Leading zeros are never significant — they only locate the decimal point, so 0.0034 has two. Trailing zeros after a decimal point are significant, so 2.50 has three, signalling precision to the hundredths. Trailing zeros in a whole number with no decimal point are ambiguous: 1,500 could be two, three or four significant figures, which is one reason scientific notation, where the ambiguity disappears, is preferred for careful work.
Significant figures in calculations
The point of significant figures is to stop calculations inventing precision. For multiplication and division, the result should carry as many significant figures as the least precise input: 4.0 times 2.51 is reported as 10, not 10.04, because 4.0 has only two. For addition and subtraction, the result is rounded to the least precise decimal place. A practical rule is to keep extra digits through intermediate steps and round only at the end, so that rounding does not accumulate. This keeps a reported answer honest about the quality of the data behind it.
Key facts
At a glance
- Definition: digits in a measurement that carry real precision information
- Non-zero digits: always significant
- Captured zeros: zeros between non-zero digits count
- Leading zeros: never significant — they only place the decimal
- Trailing decimal zeros: significant (2.50 has three)
- Calculations: result limited by the least precise input
Common misconceptions
What people often get wrong
Often heard: Leading zeros, such as in 0.0034, are significant figures.
Actually: They are not. Leading zeros merely locate the decimal point. In 0.0034 only the 3 and 4 are significant, giving two significant figures.
Often heard: Adding more decimal places always makes a result more accurate.
Actually: Extra digits beyond the measurement’s precision are meaningless and misleading. Writing 24.300 when a ruler reads to the millimetre falsely implies precision the instrument lacks.
Often heard: A calculation can have more significant figures than its inputs.
Actually: It cannot honestly. The result of a multiplication or division should carry no more significant figures than the least precise value used in it.
