Significant Figures and Rounding Calculator
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Significant Figures and Rounding Calculator
Counts the significant figures in a number as written, then rounds it to your choice of significant figures or decimal places. Trailing zeros are handled by the standard convention rather than guessed.
The convention: all nonzero digits count, zeros between them count, leading zeros never count, and trailing zeros count only when a decimal point is present. So 1200 has two significant figures, 1200. has four, and 0.0700 has three. If you mean 1200 to four figures, write 1200. or 1.200e3.
How to use this tool
Type the number exactly as it appears in your source, because the significant figure count depends on how it is written, not just its value. The tool reports the count, then rounds to your chosen number of significant figures and separately to your chosen number of decimal places, and shows the full precision scientific form for comparison.
The as written part is the point. 1200, 1200. and 1.200e3 are the same value carrying different claims about precision, and the tool treats them differently because the convention does.
The rules, and the one ambiguous case
All nonzero digits are significant. Zeros trapped between nonzero digits are significant. Leading zeros are never significant, they only set the scale, which is why 0.00456 has three figures. Trailing zeros are significant when a decimal point is present, so 0.0700 has three and 100.0 has four.
The ambiguity is trailing zeros with no decimal point. Written as 1200, there is no way to know whether the zeros were measured or are placeholders. The convention, which this tool follows, is to treat them as not significant, giving two figures. If you measured to four figures, write 1200. with the point, or 1.200e3, and the claim becomes explicit.
Why rounding to figures beats rounding to decimals
Decimal places are about position, significant figures are about information. A survey distance of 1234.5678 m rounded to three decimal places is 1234.568, still eight digits of claimed precision. Rounded to three significant figures it is 1230, which honestly reflects an instrument good to roughly one part in a thousand.
This is why measurement reporting runs on significant figures. The rule of thumb for calculations is that a result should not carry more significant figures than the least precise input, because arithmetic cannot create precision that was never measured.
A worked check you can repeat on paper
Take the speed of light, 299792458 m per s, and round to four significant figures. The first four digits are 2997, the next digit is 9, so round up to 2998, and restore the scale: 299800000. The tool returns exactly that, and its scientific form, 2.998 x 10^8, carries the four figures without any ambiguous zeros at all.
Mistakes that catch people out
Claiming trailing zeros that were never measured. Writing a rough 1200 as 1200.0 asserts five figure precision. Fix: write only the digits you can stand behind.
Rounding intermediate results. Round at each step of a long calculation and the errors stack. Fix: carry full precision through and round once at the end, which is also how this sites calculators work internally.
Treating leading zeros as significant. 0.00456 has three figures, not six. Fix: leading zeros locate the decimal point, nothing more.
Reporting a mean to more figures than the data. Averaging ten readings taken to three figures does not produce a six figure answer. Fix: the result inherits the precision of the measurements.
How this was checked
The counter was tested against the standard teaching set: 1234 giving four, 0.00456 giving three, 1.200 giving four, 1200 giving two, 1200. giving four, 100.0 giving four and 0.0700 giving three. The rounder was tested on values spanning nine orders of magnitude, including 1234.5678 to three figures giving 1230, 0.00123456 to three giving 0.00123, 9.999 to two giving 10, and the speed of light case above. Negative numbers round symmetrically.
Related Calculators and Reference
Scientific and engineering forms of the same number are the subject of the Scientific and Engineering Notation Converter. Measurement precision in the field shows up in the Length and Distance Converter, where the US survey foot question is precisely a significant figures problem at the 2 ppm level. For percent error against a true value, use the Percentage Calculator.