Sig Fig Calculator
With number 0.00453, round to how many figures 2, sig fig comes to 0.004500 — rounded value. It is reached in 5 steps, the last of which is round(0.00453 / 0.0001) * 0.0001, and each one is printed on the page with its numbers filled in. The formula is the one published by NIST SP 811, not an approximation fitted to it.
How many significant figures a number has and what it rounds to, with the leading, trailing and captive zeros counted by the rules that decide them.
Formula and sources checked · How we check
Number 0.005, Round to how many figures 2
0.004500
Rounded value for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Rounded to that many figures
round(0.00453 / 0.0001) * 0.00010.005- The digits themselves
abs(0.0045) / 10 ^ -34.5- Power of ten in scientific notation
-3- Decimal places that leaves
max(0, 2 - -3 - 1)4 places- Implied uncertainty, half the last place
abs(0.0001) / 20 ±
Worked example
0.00453 has three significant figures: the two leading zeros only place the decimal point and count for nothing. Rounded to two it is 0.0045, which is 4.5 × 10⁻³ and implies the true value lies within 0.00005 of it. Written 0.004530 it would have four, because a trailing zero after the point is a claim about precision.
How to work it out yourself
- 1.Every non-zero digit counts.
- 2.Zeros between non-zero digits count — 4,005 has four figures.
- 3.Leading zeros never count: they place the decimal point. 0.00453 has three figures, not five.
- 4.Trailing zeros after a decimal point count, because writing them is a claim about precision. 4.530 has four figures and 4.53 has three.
- 5.Trailing zeros in a whole number are ambiguous: 4,500 could be two figures or four. Scientific notation removes the ambiguity, which is why measurements are written that way.
The formula
- Rounded to that many figures
round(0.00453 / 0.0001) * 0.0001 - The digits themselves
abs(0.0045) / 10 ^ -3 - Power of ten in scientific notation
- Decimal places that leaves
max(0, 2 - -3 - 1) - Implied uncertainty, half the last place
abs(0.0001) / 2
Source: NIST SP 811 — guide for the use of the International System of Units, BIPM — the SI Brochure on expressing measurement results
Questions people actually ask
- How many significant figures does 0.00450 have?
- Three. The two leading zeros place the decimal point and count for nothing; the 4 and the 5 count; the trailing zero counts because it sits after the decimal point and someone chose to write it. Drop it and you have claimed less precision than you measured.
- Do trailing zeros count?
- After a decimal point, always — 4.530 has four figures. In a whole number, nobody can tell: 4,500 might be measured to the nearest hundred or the nearest unit. That is why 4.5 × 10³ and 4.500 × 10³ exist, and why a lab writes measurements in scientific notation rather than trusting a reader to guess.
- What are the rules for arithmetic?
- Multiplication and division keep the figures of the least precise input: 2.4 × 3.14159 is 7.5, not 7.53982. Addition and subtraction keep decimal places instead, not figures: 12.11 + 0.9 is 13.0. Mixing the two rules is the commonest mistake, because the two operations count different things.
- What does rounding to two significant figures actually claim?
- That the true value is within half of the last place kept. 0.0045 to two figures claims the value lies between 0.00445 and 0.00455. Writing more figures than the measurement supports claims a precision the instrument never had, which is what the rules exist to prevent.
- Is 0.5 rounded up or to the even digit?
- This page rounds half away from zero, which is what a calculator keyboard and most school teaching do. NIST and most scientific software round half to even instead — 2.5 becomes 2, 3.5 becomes 4 — because always rounding up biases a long series of measurements upward. On a single figure the two agree except exactly at the half.
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