Significant Figures Calculator — round to N sig figs

How it works

Significant figures (or significant digits) are the digits in a number that carry real information about its precision. You count them starting from the first non-zero digit and keep going to the end of the measured part. Rounding to N significant figures keeps the first N of them and rounds off the rest.

The rules for what counts:

• All non-zero digits are significant.
• Zeros between non-zero digits are significant (the 0 in 105).
• Leading zeros are not significant — they only place the decimal point (0.0041 has two sig figs).
• Trailing zeros after a decimal point are significant (4.50 has three).

To round, find where the Nth significant figure falls and round at that position.

Worked example

Round π = 3.14159 to 3 significant figures. The first three significant digits are 3, 1 and 4; the next digit is 1 (below 5), so round down: 3.14.

For a large number, 12345 to 2 significant figures: keep 1 and 2, and the next digit 3 rounds down, giving 12000 — the trailing zeros are placeholders, not significant. And 0.04052 to 2 significant figures: the leading zeros don't count, so the first two significant digits are 4 and 0; the next digit 5 rounds up, giving 0.041.

Frequently asked questions

How do I count significant figures?

Start at the first non-zero digit and count every digit to the end of the number's measured part. 0.00230 has three significant figures (2, 3, 0 — the trailing zero counts, the leading zeros don't); 1004 has four. Non-zero digits and "sandwiched" zeros always count.

Do leading and trailing zeros count?

Leading zeros (before the first non-zero digit) never count — they just set the scale, so 0.0057 has two sig figs. Trailing zeros after a decimal point do count, because they indicate precision: 2.50 has three sig figs. Trailing zeros in a whole number like 1200 are ambiguous, which is why scientific notation is clearer.

What's the difference between significant figures and decimal places?

Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. 0.04052 has five decimal places but rounding it to 2 *significant figures* gives 0.041, while rounding to 2 *decimal places* gives 0.04 — different questions with different answers.

Why do significant figures matter?

They communicate how precise a measurement is. Reporting 3.14 says you're confident to three figures; reporting 3.14159 claims six. In science and engineering, carrying too many figures overstates precision, and dropping too many loses it — so results are usually quoted to the number of significant figures the measurement supports.

How many significant figures should a calculation keep?

A common rule: a result should have no more significant figures than the least precise value that went into it. If you multiply 4.5 (2 sig figs) by 2.11 (3), the answer 9.495 is rounded to 2 sig figs — 9.5. That prevents a calculation from looking more precise than its inputs.

How does scientific notation show significant figures?

The mantissa displays them exactly. 4.50 × 10³ unambiguously has three significant figures, while the plain number 4500 could have two, three or four. That's why scientific notation is the standard way to state a value's precision without ambiguity.