Significant Figures Calculator

Enter any number — including scientific notation like 1.23e4 — to count its significant figures and round it to a target number of sig figs.

Result

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Enter a number and click Count & Round

Quick Examples

What Are Significant Figures?

Significant figures (often shortened to sig figs) are the digits in a number that carry real, meaningful precision about a measurement. They tell the reader which digits were actually measured and which are just placeholders. A significant figures calculator counts those digits and rounds numbers to a chosen precision.

The core idea: 2.5 cm (2 significant figures) is less precise than 2.50 cm (3 significant figures). The trailing zero claims the instrument actually read that digit. Knowing which zeros count and which do not is the entire skill — the five rules below cover every case.

The Five Significant Figure Rules

Rule 1: All non-zero digits are significant

Every digit from 1 through 9 counts, always. The number 483 has 3 significant figures; 7.195 has 4. This is the base rule — everything else concerns zeros.

Rule 2: Zeros between non-zero digits (captive zeros) are significant

A zero sandwiched between non-zero digits carries measured precision. The number 1001 has 4 significant figures; 20.06 has 4.

Rule 3: Leading zeros are never significant

Zeros to the left of the first non-zero digit only position the decimal point. The number 0.004560 has 4 significant figures (4, 5, 6, and the trailing zero); the two leading zeros do not count. Similarly, 0.0005 has just 1 significant figure.

Rule 4: Trailing zeros after a decimal point are significant

A zero at the end of a number with a decimal point states measured precision and always counts. The number 7.00 has 3 significant figures; 10.10 has 4.

Rule 5: Trailing zeros in a whole number are ambiguous

A zero at the end of a number without a decimal point — like 1200 — may or may not be significant: it could have been rounded to the nearest hundred or measured to the ones place. Standard convention: count only the non-zero digits, so 1200 has 2 significant figures.

To remove the ambiguity, use one of these forms:

Add a decimal point: 1200. explicitly states 4 significant figures.
Use scientific notation: 1.2 × 10³ states 2, 1.20 × 10³ states 3, 1.200 × 10³ states 4.
Add a bar over the last significant zero: 1200 indicates 3 significant figures.

Exact Numbers

Exact numbers have effectively infinite significant figures and never limit the precision of a calculation. They come in three forms:

Counts: 24 students, 7 apples — exact by definition.
Defined quantities: 100 cm in a meter, 60 seconds in a minute — definitions, not measurements.
Coefficients: the 2 in 2πr, stoichiometric coefficients in a balanced equation.

When a calculation mixes a measurement with an exact number, only the measurement limits the sig figs.

How to Round to N Significant Figures

Rounding to significant figures keeps the first N meaningful digits and replaces the rest:

Identify the first N significant digits (leading zeros do not count).
Look at the very next digit after the last kept digit.
If the next digit is less than 5, leave the last kept digit unchanged.
If the next digit is 5 or greater, round the last kept digit up by one.
Replace all remaining digits with zeros (or drop them after a decimal point).

9.05675 to 3 sig figs → 9.06. Kept digits 9, 0, 5; the next digit 6 rounds the 5 up to 6. (Trailing zeros in 9.06000 add no value, so they drop.)
0.01234 to 3 sig figs → 0.0123. Leading zeros are skipped, so kept digits are 1, 2, 3; the next digit 4 leaves the 3 unchanged.

Whole-number caution: 1015 rounded to 2 significant figures becomes 1000 — the remaining digits are placeholders. Write 1.0 × 10³ to state 2 sig figs explicitly.

Significant Figure Count Reference Table

Number	Sig Figs	Which Rule Applies
483	3	All non-zero digits count
1001	4	Captive zeros count
0.004560	4	Leading zeros do not count; decimal trailing zero does
7.00	3	Trailing zeros after decimal point count
10.10	4	Captive zero and decimal trailing zero count
1200	2	Whole-number trailing zeros are ambiguous — count 1, 2
1200.	4	Decimal point makes trailing zeros significant
0.0005	1	Leading zeros do not count
6.022e23	4	Exponent does not count; mantissa digits do
1.2300e4	5	All five mantissa digits count (decimal trailing zeros)

Significant Figures in Calculations

Measurements propagate their precision through calculations. Two rules govern every operation:

Multiplication and division: fewest significant figures

The result keeps the fewest significant figures of any input — the least precise measurement sets the ceiling for the whole calculation.

sig figs(result) = min(sig figs of all inputs)

Example: 12.5 × 3.24 = 40.5. Both inputs have 3 significant figures, so the answer keeps 3: 40.5.

Addition and subtraction: fewest decimal places

The result keeps the fewest decimal places of any input — a different rule, because these operations shift precision by place value rather than digit count.

decimal places(result) = min(decimal places of all inputs)

Example: 45.2 + 8.35 + 2.1 = 55.65. The fewest decimal places is one (from 45.2), so the answer is 55.7.

Never round intermediate steps in a multi-step calculation — carry extra digits through the work and round only the final answer, or cumulative rounding errors will distort the result.

Why Significant Figures Matter

Significant figures prevent false precision — claiming more accuracy than your measurements support. A balance that reads to 0.1 g cannot justify reporting a density of 2.468 g/cm³; the correct 3-sig-fig report is 2.47 g/cm³.

They matter most in:

Chemistry: lab reports and titration results must match instrument precision.
Physics: experimental measurements and error analysis need stated precision.
Engineering: tolerances and safety margins depend on honest precision.
Medicine: dosages and lab values are reported to clinically meaningful digits, never more.

Common Significant Figure Mistakes

Mistake 1: Counting leading zeros. 0.004560 has 4 significant figures, not 6 — the leading zeros never count.
Mistake 2: Dropping decimal trailing zeros. Writing 7.00 as 7 changes a 3-sig-fig measurement into a 1-sig-fig one.
Mistake 3: Treating whole-number trailing zeros as significant. 1200 has 2 significant figures by default; use 1200. or 1.200 × 10³ for more.
Mistake 4: Using the wrong calculation rule. Addition and subtraction use fewest decimal places, not fewest sig figs — a different rule from multiplication and division.
Mistake 5: Rounding intermediate steps. Carry extra digits and round once, at the end.
Mistake 6: Counting the exponent. In 6.022e23, the "23" is a scale factor, not a measured digit. Only the mantissa 6.022 counts: 4 sig figs.
Mistake 7: Confusing sig figs with decimal places. 0.0123 has 3 significant figures but 4 decimal places.

Frequently Asked Questions

What are significant figures?

Significant figures (sig figs) are the digits in a number that carry real precision: all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point. Leading zeros are never significant. For example, 0.004560 has 4 significant figures (4, 5, 6, and the trailing 0).

How many significant figures are in 0.004560?

Four. The two leading zeros (0.00) only position the decimal point and never count. The digits 4, 5, and 6 are non-zero and significant, and the trailing zero after the decimal point counts.

Are trailing zeros significant in a whole number like 1200?

Usually not: 1200 has 2 significant figures (1 and 2), and the zeros are ambiguous. Write 1200. for 3 significant figures, or 1.200 x 10^3 for 4.

How do I round a number to a given number of significant figures?

Keep the target count of meaningful digits, then look at the next digit: if it is less than 5, leave the last kept digit unchanged; if it is 5 or greater, round the last kept digit up. For example, 9.05675 to 3 significant figures becomes 9.06.

What are the rules for significant figures in calculations?

For multiplication and division, the result keeps the fewest significant figures of any input: 12.5 x 3.24 = 40.5 (both inputs have 3 sig figs). For addition and subtraction, the result keeps the fewest decimal places: 45.2 + 8.35 + 2.1 = 55.65, rounded to 55.7.

Do exact numbers have significant figures?

Exact numbers have effectively infinite significant figures and never limit a calculation: counts (24 students), defined quantities (100 cm in a meter), and stoichiometric coefficients are exact. Multiplying a 3-sig-fig measurement by the exact count 24 keeps 3 significant figures.

Conclusion

Significant figures boil down to five counting rules: non-zero digits always count, captive zeros count, leading zeros never count, decimal trailing zeros count, and whole-number trailing zeros are ambiguous without a decimal point or scientific notation. Exact numbers never limit precision; calculations inherit the weakest precision.

Rounding to N significant figures is a three-step reflex: keep N meaningful digits, check the next digit, and round up on 5 or greater. Use the significant figures calculator at the top of this page to count sig figs and round any number instantly, including scientific notation like 1.23e4.