Significant figures are how a measured number says how much of it is real. This calculator counts them in any number exactly as written, rounds a number to a chosen count, and works through arithmetic expressions applying the sig fig rules step by step, so you can see which rule set the precision at each stage. All arithmetic runs on the exact decimal digits typed, never on a binary approximation.
Type the number exactly as it is written, including trailing zeros and the decimal point: they carry the meaning. Scientific notation such as 1.200e3 is accepted.
How to use this calculator
- Count mode answers “how many significant figures are in this number?” Type the number exactly as written. 1200 and 1200. are different claims, and the calculator reads them differently, because the decimal point is part of the claim.
- Round mode rounds any number to a chosen count of significant figures, from 1 to 15, and shows the digit that decided the rounding.
- Calculate mode evaluates an expression such as 2.34 * 1.5 + 0.006 with the sig fig rules applied: addition and subtraction keep decimal places, multiplication and division keep significant figures, and the precision is tracked through every step before the final answer is rounded once.
- Read the big answer first, then the table and the step list, which show exactly where the precision came from.
The rules
Counting significant figures
- Non-zero digits always count. 405 has three significant figures; the zero between the 4 and the 5 (a captive zero) counts too.
- Leading zeros never count. In 0.00450, the zeros before the 4 only position the decimal point.
- Trailing zeros count only when a decimal point is written. 1200 has two significant figures: the zeros are placeholders. 1200. has four, and 1200.0 has five. The decimal point is the writer saying “these zeros were measured”.
- In scientific notation, the mantissa digits count. 1.200 × 103 has four significant figures; the × 103 only sets the size. Every mantissa digit written is significant, which is why scientific notation is the honest way to write a number like 1200 when the zeros matter.
- Exact numbers have unlimited significant figures. Counts (24 students) and defined quantities (exactly 100 cm in a metre by definition) never limit a result. They are not measurements.
Arithmetic rules
Through a longer calculation, keep guard digits: carry the full value from step to step and track which precision each operation allows, then round once, at the end. Rounding every intermediate result throws away real precision and can shift the final digit.
Worked examples
Example 1: counting, 0.00450
The zeros before the 4 are leading zeros and never count. The 4 and the 5 count. The final 0 counts because it sits after a decimal point, so it records a measurement precise to the hundred-thousandths place. Total: 3 significant figures, written in scientific notation as 4.50 × 10−3. This is the preloaded count example.
Example 2: one number, three claims
1200 has 2 significant figures. 1200. has 4. 1.200 × 103 has 4, stated unambiguously. Same size, three different precision claims; that difference is the whole point of the rules.
Example 3: rounding 12.345
To 4 significant figures, 12.345 becomes 12.35: the first dropped digit is exactly 5 and this calculator rounds halves away from zero, working on the exact digits typed. (A tool that first converts 12.345 to binary floating point can see 12.3449999… and answer 12.34; the decimal digits you typed say 12.35.) To 3 significant figures it becomes 12.3. Try both in Round mode.
Example 4: addition is about decimal places
12.11 + 18.0 + 1.013 = 31.123 before rounding. The least precise term is 18.0, precise only to the tenths place, so the answer is 31.1, even though two of the terms were known to the hundredth and thousandth. This is the preloaded expression.
Example 5: multiplication is about significant figures
123 × 0.0456 = 5.6088 before rounding. Both factors have 3 significant figures, so the answer keeps 3: 5.61. The long decimal tail of 5.6088 is arithmetic, not knowledge.
Example 6: mixed operations
2.34 × 1.5 + 0.006: the multiplication comes first, 3.51, and with 2 significant figures in 1.5 the product is precise to the tenths place. Adding 0.006 (thousandths) cannot beat tenths, so 3.516 rounds to 3.5. Each step’s rule is shown when you run it in Calculate mode.
Reading your results
In Count mode, the headline is the count, and the notes name every class of digit in your number: which zeros were leading, which were captive, and whether the trailing zeros counted, with the reason in each case. The last-significant-digit place tells you the precision the number claims: a number precise to the hundredths place was measured with a finer instrument than one precise to the tens place.
In Round mode, the answer is shown in ordinary notation and in scientific notation. Scientific notation is the form that never lies about trailing zeros: 1.0 × 104 says two significant figures in a way the plain 10000 cannot.
In Calculate mode, read the steps underneath the answer. Each line shows one operation, its unrounded result, and the rule that fixed the precision carried forward. The final rounding happens once, at the end, to the precision the chain actually earned.
Common mistakes
- Counting leading zeros. 0.00450 does not have five significant figures; it has three. Leading zeros are signposts, not measurements.
- Treating every trailing zero the same. The zeros in 1200 are placeholders until a decimal point (1200.) or scientific notation (1.200 × 103) promotes them. The zeros in 12.30 always count.
- Using decimal places for multiplication. 123 × 0.0456 is a significant-figure question (3 sf, answer 5.61), not a decimal-place question. The two rules answer different operations.
- Rounding at every step. Rounding 3.51 to 3.5 before adding 0.006 happens to agree here, but in longer chains step-rounding compounds and moves final digits. Track the precision, round once.
- Reporting the calculator’s raw digits. Writing 5.6088 as the answer to 123 × 0.0456 claims a precision the inputs never had. The digits are free; the knowledge is not.
- Letting an exact number limit a result. Dividing a measurement by exactly 3 (three equal parts) does not cap the answer at one significant figure; exact counts and definitions carry unlimited precision.
Limitations
- A trailing-zero count with no decimal point is genuinely ambiguous in the wild: some writers mean 1200 as an exact count. This calculator applies the standard convention (2 significant figures) and says so; scientific notation removes the ambiguity entirely.
- Exact halves round away from zero here, the common school and laboratory convention. Some fields use round-half-to-even instead; on an exact half the last digit can differ by one.
- Calculate mode covers + − × ÷ and brackets. Powers, roots and functions belong to the Scientific Calculator linked below; their sig fig handling follows the same smallest-count spirit but is not tracked here.
- Significant figures are a reporting convention, a shorthand for measurement uncertainty. They do not create accuracy: a result is never better than the instrument and method behind the least precise input.
Frequently asked questions
How many significant figures are in 0.00100?
Three. The leading zeros position the decimal point and never count; the 1 counts; the two trailing zeros count because they sit after a decimal point, recording precision to the hundred-thousandths place.
Why does 1200 have 2 significant figures but 1200. has 4?
The decimal point is a claim. Without it, the zeros in 1200 are read as placeholders that merely make the number big. Writing 1200. says the writer measured right down to the ones place, so both zeros count. Scientific notation says it without ambiguity: 1.200 × 103.
Are trailing zeros after a decimal point always significant?
Yes. In 12.30 the final zero was written deliberately and records a finer measurement than 12.3 would. Deleting it changes the claim, not just the look.
Do exact numbers have significant figures?
No limit applies. Counts (3 trials, 24 students) and defined constants (1000 m in a kilometre, by definition) are exact, so they never cap the precision of a result. Only measured numbers do.
Should I round after every step of a calculation?
No. Carry guard digits through the steps and round once at the end. This calculator tracks the precision each operation allows and applies one final rounding; rounding every intermediate value discards real precision and can move the last digit of the answer.
What is the difference between significant figures and decimal places?
Decimal places count digits after the point; significant figures count digits from the first non-zero digit. They govern different operations: addition and subtraction follow decimal places (really, decimal position), multiplication and division follow significant figures.
Related calculators
- Math calculators
- Scientific Calculator: full expressions with powers, roots, trig and logs.
- Rounding Calculator: ordinary rounding to decimal places, whole numbers and nearest values.
- Long Division and Decimal Calculator: exact decimal results with the division steps shown.
Method: counting by the standard written-form rules (leading zeros never significant; captive zeros significant; trailing zeros significant only with a decimal point or in a scientific-notation mantissa); addition and subtraction rounded to the least precise decimal place, multiplication and division to the smallest significant-figure count, with guard digits carried and one final rounding, halves away from zero. All arithmetic is performed on the exact decimal digits entered. Last reviewed: 21 October 2026.
Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice.