Significant Figures Calculator — Step-by-Step Solutions

The Significant Figures Calculator counts significant figures in any number, rounds to a specified number of sig figs, applies significant figure rules to arithmetic operations, and converts between standard and scientific notation.

Enter a number to see which digits are significant (highlighted in the output), or perform calculations with proper sig fig rules applied. The calculator handles leading zeros, captive zeros, and trailing zeros correctly.

Enter a number

Significant Figures

—

Your calculations will appear here

How to Use the Significant Figures Calculator

Count Sig Figs: type a number exactly as written, including trailing zeros and any decimal point (0.00340, 1200, 1200.). The calculator counts the significant figures and highlights each digit.
Round to N Sig Figs: enter the number and how many significant figures to keep. Rounding always keeps the leading digits: 98765 to 3 sig figs is 98800.
Arithmetic with Sig Fig Rules: enter Value A and Value B, choose add, subtract, multiply or divide, and get the result rounded by the right rule. Type each value exactly as measured (1.20, not 1.2) so that trailing zeros count.
Scientific Notation: enter a number to see it as a coefficient between 1 and 10 times a power of 10.

Formula and Theory

Significant figures are the digits in a measured number that carry information about its precision. They include every non-zero digit, zeros between non-zero digits, and trailing zeros after a decimal point. Leading zeros never count, because they only place the decimal point. So 0.00340 has 3 significant figures, 3.0 has 2 and 100.0 has 4.

Trailing zeros in a whole number without a decimal point are ambiguous. By the usual convention in this calculator, 1200 has 2 significant figures, while 1200. (with a point) has 4. Scientific notation removes the ambiguity: 1.20 x 10^3 has 3.

When combining measurements, the answer cannot be more precise than the inputs. For multiplication and division, round the result to the number of significant figures of the input with the fewest. For addition and subtraction, round to the fewest decimal places, regardless of the number of significant figures.

Do the rounding only at the end of a multi-step calculation, carrying an extra digit through the intermediate steps. Exact counts and defined constants (12 eggs in a dozen, 100 cm in a metre) have unlimited significant figures.

Worked Examples

Example 1: Counting significant figures

Problem: How many significant figures are in 0.00340, 1200, 1200., 5008 and 3.0?

Solution: 0.00340: the leading zeros do not count, but the 3, 4 and the trailing 0 after the decimal do, so 3. 1200: the trailing zeros have no decimal point, so only 1 and 2 count: 2. 1200.: the decimal point makes all four significant: 4. 5008: the zeros are between non-zero digits, so 4. 3.0: the trailing zero follows a decimal point: 2.

Answer: 3, 2, 4, 4 and 2

Example 2: Rounding to significant figures

Problem: Round 3.14159 to 3 significant figures, 0.004567 to 2, and 98765 to 3.

Solution: 3.14159: keep 3.14 and look at the next digit, 1, so it rounds down: 3.14. 0.004567: the first significant digit is 4, so keep 0.0045 and the next digit is 6, which rounds up: 0.0046. 98765 to 3 sig figs: keep 987 and the next digit 6 rounds the 7 up to 8: 98800.

Answer: 3.14, 0.0046 and 98800

Example 3: Multiplication

Problem: Calculate 4.56 x 1.4 with the right number of significant figures.

Solution: The raw product is 4.56 x 1.4 = 6.384. 4.56 has 3 significant figures and 1.4 has 2, so the answer keeps the smaller number, 2: 6.4.

Answer: 6.4

Example 4: Addition

Problem: Calculate 12.11 + 0.3 with the right precision.

Solution: The raw sum is 12.41. 12.11 has 2 decimal places and 0.3 has 1, so the result is limited to 1 decimal place: 12.4. Note that this is about decimal places, not significant figures.

Answer: 12.4

Example 5: Division and scientific notation

Problem: Calculate 22.4 / 1.25, then write 45600 in scientific notation.

Solution: 22.4 / 1.25 = 17.92. Both numbers have 3 significant figures, so the answer has 3: 17.9. For 45600, move the decimal 4 places left: 4.56 x 10^4.

Answer: 17.9 and 4.56 x 10^4

Frequently Asked Questions

What are significant figures?

They are the digits of a number that are meaningful as a measurement. They show how precisely something was measured, so 2.50 g claims more precision than 2.5 g.

Do trailing zeros count?

After a decimal point, yes: 2.50 has 3. In a whole number without a decimal point they are ambiguous and are treated as not significant, so 1200 has 2. Write 1.20 x 10^3 or 1200. to be explicit.

Do leading zeros count?

Never. They only show where the decimal point is. 0.0052 has 2 significant figures.

What are the rules for adding and multiplying?

For multiplying and dividing, the answer has as many significant figures as the input with the fewest. For adding and subtracting, the answer has as many decimal places as the input with the fewest.

Do exact numbers have significant figures?

Counted and defined quantities, like 3 beakers or 100 cm in 1 m, are exact and do not limit the precision of the result.

Why does the arithmetic mode need strings like 1.20?

Because the number of significant figures depends on how a number is written. 1.2 and 1.20 are the same value but have 2 and 3 significant figures, so the typed form matters.