How many digits a number really claims, and how many an answer may keep.
Count them, or round to them
Ambiguity is reported.
Write a trailing point — 1500. — when the zeros are measured digits.
1500
2 significant figures
Ambiguous as written — this is the minimum reading. See the alternatives below.
Significant figures
2
minimum reading
Decimal places
0
what an addition would be limited to
Scientific notation
1.5 × 10³
which removes the ambiguity
Rounded
—
ask for a number of figures
Digit by digit
Each digit with whether it is significant and why
Digit
Counts?
Why
1
yes
a non-zero digit
5
yes
a non-zero digit
0
no
a trailing zero with no decimal point — ambiguous, not counted here
0
no
a trailing zero with no decimal point — ambiguous, not counted here
What it could mean
Each possible reading of the trailing zeros, with the scientific notation that would state it
2 sf
1.5 × 10³
the minimum reading — the one assumed here
3 sf
1.50 × 10³
if 1 of the trailing zeros is a measured digit
4 sf
1.500 × 10³
if 2 of the trailing zeros are measured digits
Scientific notation states the precision explicitly, which is the practical reason to use it for measurements.
Carrying it through a calculation
Multiplying or dividing: the answer keeps the FEWEST significant figures of any input. With 2, a product involving this number can carry at most 2.
Adding or subtracting: the answer keeps the fewest DECIMAL PLACES, not figures. This number has 0.
Exact numbers — counts, defined constants, conversion factors — have infinite significant figures and never limit the answer. Twelve eggs is exactly twelve.
1500 is AMBIGUOUS. Written without a decimal point, its trailing zeros could be measured digits or could be placeholders, and the notation cannot say which. This page assumes the minimum — 2 figures — because under-claiming precision can be corrected by whoever took the measurement, while nothing downstream can tell an invented digit from a measured one.
Scientific notation removes the ambiguity entirely, which is the practical reason to use it: 1.5 × 10³, 1.50 × 10³ and 1.500 × 10³ are three different claims about how carefully something was measured.
Significant figures are a statement about MEASUREMENT, not about arithmetic. They say how much of a number was actually observed, and carrying more through a calculation asserts a precision that was never there.
The two propagation rules are different, and mixing them is the commonest error: 12.1 + 0.033 is 12.1 — the fewest decimal places, one — not 12.133 and not 12.
Counted on the digits as written, so a trailing zero is not lost the way a floating-point value would lose it.
What this tool shows
1500 might be two significant figures, or three, or four. The way it is written cannot tell you, so this page says so rather than choosing quietly — and shows the scientific-notation form that would have removed the doubt.
How many significant figures a number carries
Which digits count, and why each one does or does not
When trailing zeros make the count ambiguous
The scientific notation that removes the ambiguity
Rounding to a requested number of figures
The decimal places an addition would be limited to
Each digit marked Both propagation rules Ambiguity reported, not hidden Scientific form shown
Counted on the digits as written, not through a float.
Updated 7 September 2026 · Works in any browser, no installation
Start at the first non-zero digit and count to the last significant one. Leading zeros never count — 0.00450 has three figures, not five — because they only place the decimal point. Zeros between digits always count. Trailing zeros count when a decimal point is written, which is why 2.50 claims three figures and 2.5 claims two.
At a glance
Formula shown
Count from the first non-zero digit to the last significant one. Leading zeros never count; embedded zeros always do; trailing zeros count when a decimal point is written and are ambiguous without one. For a product or quotient the answer takes the fewest significant figures of any input; for a sum or difference it takes the fewest decimal places.
Scenario support
Reporting a lab result to the precision the instrument justifies; checking whether a quoted figure claims more accuracy than its source; deciding how to write a rounded total so the reader knows what was measured.
Educational estimate
Planning support from the values you enter — not professional advice.
Which digits count
Significant figures record how precisely something was measured. A digit is significant when it carries information about the measurement rather than about where the decimal point sits.
Leading zeros never count. 0.00450 has three significant figures. Write it as 4.50 × 10⁻³ and the leading zeros vanish without changing the number, which is the proof that they were never carrying anything.
Zeros between digits always count. 1002 has four. There is no way to have measured the 2 without also having measured the two zeros in front of it.
Trailing zeros count when a decimal point is written. 2.50 has three, and that final zero is a claim: it says the hundredths place was measured and found to be zero. Writing 2.5 makes a weaker claim about the same quantity.
Why 1500 is ambiguous
1500 might have been measured to the nearest 100, the nearest 10, or the nearest 1. Written that way it carries two, three or four significant figures, and the notation has no way to say which.
This is a real defect in the convention, not a subtlety. The page reports it rather than choosing quietly, takes the smallest defensible reading, and lists what each alternative would mean.
The direction of that default is deliberate. Under-claiming precision can be corrected by whoever took the measurement; over-claiming cannot be detected at all downstream, because nothing in a number distinguishes a measured digit from an invented one.
Scientific notation removes the ambiguity outright. 1.5 × 10³ is two figures, 1.50 × 10³ is three, 1.500 × 10³ is four, and no reader has to guess. That is why the page shows the scientific form beside the count.
Multiplying and adding use different rules
This is where lab reports go wrong, and it goes wrong because the two rules look interchangeable and are not.
Multiplying or dividing: the answer takes the FEWEST SIGNIFICANT FIGURES of any input. 4.5 × 2.03 = 9.135 on the calculator, reported as 9.1, because 4.5 only had two figures to give.
Adding or subtracting: the answer takes the fewest DECIMAL PLACES of any input. 12.1 + 0.033 = 12.133 on the calculator, reported as 12.1 — not 12.133, and not 12 either. Applying the figures rule here would give 12, which throws away a digit that 12.1 genuinely had.
The reason they differ is that addition aligns the decimal points, so precision is limited by place value, while multiplication combines relative errors, so it is limited by proportion. The page reports both the figure count and the decimal-place count for this reason.
Exact numbers have no limit
Some numbers are not measurements at all, and they impose no limit on the answer.
Counts. Three flasks is exactly three. Dividing a measured mass by 3 does not cost you a significant figure.
Defined conversions. One inch is exactly 25.4 mm and one hour is exactly 3600 seconds, by definition rather than by measurement. Converting units never reduces precision.
Mathematical constants. π is exact; only the version you typed is truncated. Carry more digits of it than your data has and it will not be what limits the answer.
Round once, at the end
Significant figures are a rule for reporting a result, not for computing one. Rounding intermediate values to the final precision loses digits that the later steps needed.
Carry full precision through every step, decide the figure count from the least precise input, and round once when you write the answer down. Rounding twice can shift the last digit on its own — the Rounding Calculator has the worked case.
When a rounded value has to be written in the middle of a report, keep one or two guard digits and mark them, so a reader can see which digits were carried for arithmetic and which are being claimed as measured.
What the convention cannot do
Significant figures are a shorthand, and it is worth knowing where the shorthand runs out.
It cannot express uncertainty precisely. Three figures says the answer is good to about a part in a thousand, but 1.00 and 9.99 both have three figures and their relative precisions differ by a factor of ten. Where the uncertainty is actually known, quote it — 4.52 ± 0.03 says more than 4.52 ever can.
It cannot survive a badly conditioned subtraction. Subtract 1.234 from 1.235 and both inputs had four figures while the answer, 0.001, has one. The rules give the right count here, but they give no warning that three figures just disappeared.
And it cannot distinguish precision from accuracy. A miscalibrated instrument will produce five consistent significant figures that are all wrong together. The convention tracks how finely you measured, never how correctly.
Sources and methodology
The convention and the alternative to it are both specified — these are the references.
Method. Everything runs on the digit string, so a trailing zero survives to be counted instead of disappearing into a float. Each digit is classified separately with the reason it is or is not significant, and the count is reported alongside the decimal-place count, because the two propagation rules need different numbers. Where trailing zeros before an implied decimal point make the count ambiguous, the page takes the smallest defensible reading and lists the alternatives with the scientific notation each would be written as. That engine is verified on every change against 61 hand-written assertions, including that the scientific-notation form always carries exactly the reported number of figures, and that rounding to n figures and counting again returns n, checked across generated numbers spanning fifteen orders of magnitude. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
RoundingAll seven rounding rules on the same number at once, so the disagreement at a tie is visible rather than buried inside whichever one your software happened to pick.
Percent ErrorPercent error against an accepted value, rounded to your significant figures, for one measurement, repeated trials, or a whole column of pairs.
Square RootThe exact square root first — 72 gives 6 root 2 — then the decimal to as many as sixty places, computed on whole numbers rather than a double.
ExponentPowers with the awkward cases right — a negative exponent is a reciprocal not a sign, a fractional one is a root, and zero to the zero is reported as contested.
Standard DeviationSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.
Root Mean SquareFor values whose sign must not cancel. Mains voltage averages zero and still boils a kettle; squaring, averaging and rooting gives the number that describes the work.
Once the number of figures is settled, the Rounding Calculator covers the second half of the question — which rule drops the digits, and what happens at a tie.
Educational use disclaimer
This is an educational tool. Significant figures are a convention for reporting precision, not a substitute for stated uncertainty; where the uncertainty is actually known, quote it directly.
Published the significant figures page reporting ambiguity instead of resolving it quietly: 1500 may be two, three or four figures and the notation cannot say which.
The minimum reading is taken by default, because under-claiming precision can be corrected by whoever measured and over-claiming cannot be detected downstream at all.
Both propagation rules are given and distinguished, since using the significant-figures rule on a sum is the commonest error a lab report contains.
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