Math · Live

Significant Figures Calculator —
count, highlight & round.

Enter any number — decimal or scientific notation — to instantly see how many significant figures it has, with every digit color-coded by the rule that applies to it, plus a clean rounding to the precision you choose.

How it worksReal-time

Inputs

Number & precision

Input numberdecimals & 1.2e-4

Round to (significant figures)

Significant figures: 4
Rounded: 0.00456
Scientific: 4.56e-3

Significant figures

4significant figures in your number

0.004560

SignificantNot significant

Rounded to 3 sig figs

0.00456

Scientific notation

4.56e-3

Plain decimal

0.00456

Step by step

Why each digit counts (or doesn’t)

4/7 significant

0
Leading zero
Leading zero (before the first non-zero digit) — not significant
0
Leading zero
Leading zero (before the first non-zero digit) — not significant
0
Leading zero
Leading zero (before the first non-zero digit) — not significant
4
Non-zero
Non-zero digit — always significant
5
Non-zero
Non-zero digit — always significant
6
Non-zero
Non-zero digit — always significant
0
Trailing (decimal)
Trailing zero with a decimal point present — significant

Field guide

The rules of significant figures.

Significant figures capture how precisely a number is known. Whether a digit “counts” comes down to four short rules, and the calculator above applies all of them to every digit you type:

All non-zero digits are significant. 1–9 always count. So 482 has 3 significant figures.
Zeros between non-zero digits are significant. These “captive” zeros count: 4002 has 4 sig figs.
Leading zeros are never significant. They only place the decimal point. 0.00456 has 3 sig figs.
Trailing zeros are significant only with a decimal point. 1.200 has 4 sig figs; 1200 (no decimal) has 2 and is ambiguous.

0.004560 → leading zeros don’t count, 4-5-6 and the trailing 0 do → 4 significant figures

Rounding to N significant figures.

To round to a target precision, keep that many significant digits starting from the first non-zero digit, then round the rest. If the first dropped digit is 5 or more, round up.

Example: Round 12,345 to 2 significant figures. The first two significant digits are 1 and 2; the next digit is 3, so we round down, giving 12,000. Because those trailing zeros aren’t significant on their own, the unambiguous way to write the answer is 1.2×10⁴ (or 1.2e+4).

12345 → 2 sig figs → 1.2 × 10⁴ = 12000

Significant figures in arithmetic.

The trickiest part of sig figs isn’t counting them — it’s knowing how many to keep after a calculation. The rule depends on the operation.

Multiplication & division

The result keeps as many significant figures as the input with the fewest significant figures.

4.56 (3 sig figs) × 1.4 (2 sig figs) = 6.384 → round to 2 sig figs → 6.4

Addition & subtraction

Here you count decimal places, not significant figures. The result keeps as many decimal places as the input with the fewest decimal places.

12.11 (2 dp) + 0.3 (1 dp) + 1.014 (3 dp) = 13.424 → round to 1 dp → 13.4

A useful habit: carry extra digits through intermediate steps and round only at the very end, so rounding errors don’t compound.

Why significant figures matter.

Sig figs communicate the honesty of a measurement. Reporting a length as 4.500 m claims you know it to the nearest millimetre; writing 4.5 m claims only the nearest tenth of a metre. Adding digits you didn’t actually measure overstates your precision, which is why labs, exams, and engineering all enforce sig-fig conventions. Scientific notation, like the form this calculator outputs, is the cleanest way to state precision without ambiguity.

Related calculators

For general rounding modes, see the Rounding Calculator; to convert to and from powers of ten, try the Scientific Notation Calculator.

Disclaimer: The significant figures calculation and rounding rules provided by this tool are for educational and reference purposes only. While mathematically accurate according to standard scientific conventions, precision handling in real-world engineering or laboratory environments should always be verified against specific field guidelines.

FAQ

Frequently asked

What are significant figures?+

Significant figures (sig figs) are the digits in a number that carry real, reliable information about its precision. They include all non-zero digits, any zeros between them, and trailing zeros when a decimal point is present. They tell you how precisely a quantity was measured or is known.

Are trailing zeros significant?+

It depends on whether there's a decimal point. In 1.200 the trailing zeros ARE significant (4 sig figs) because the decimal point shows they were measured. In 1200 with no decimal point, the trailing zeros are ambiguous and, by the common convention this calculator uses, are NOT counted (2 sig figs). Writing it as 1200. or 1.200×10³ removes the ambiguity.

Are leading zeros significant?+

No. Leading zeros only position the decimal point — they are never significant. In 0.00456 the three leading zeros don't count; the number has 3 significant figures (4, 5, and 6).

How do you round significant figures in scientific notation?+

Write the number as a mantissa times a power of ten, then keep the desired number of digits in the mantissa. Rounding 12,345 to 2 sig figs gives 1.2×10⁴ (shown as 1.2e+4). The exponent is positional and never counts toward the significant-figure total, so 1.2e-4 has 2 sig figs.

What are the sig-fig rules for addition versus multiplication?+

They differ. For multiplication and division, the result keeps as many significant figures as the input with the FEWEST sig figs. For addition and subtraction, the result keeps as many DECIMAL PLACES as the input with the fewest decimal places — you count decimal places, not sig figs.

How many significant figures does zero have?+

A bare 0 is ambiguous and is reported as 0 significant figures here. In a measured value like 0.0 or 10.0, the zeros can be significant because the decimal point and context show the precision. When precision matters, state it explicitly or use scientific notation.

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