Significant Figures Calculator

Significant figures at a glance#

Significant figures are the digits in a number that carry real precision. Four rules set the count: every non-zero digit counts; zeros between non-zero digits count; leading zeros never count; trailing zeros after a decimal point count. The calculator above rounds a number to a chosen count of significant figures.

How many significant figures does a number have?#

Apply the four rules digit by digit. So 0.00450 has 3 significant figures: the leading zeros do not count, while 4, 5 and the trailing 0 after the decimal do. A plain 1200 is ambiguous because trailing zeros with no decimal point may or may not be significant. Writing it as 1.20 x 10^3 fixes the count at 3.

How do you round to a number of significant figures?#

Keep the digits you need, then look at the next digit. If it is less than 5, leave the last kept digit as it is; if it is 5 or more, raise it by 1. So 123.456 rounded to 3 significant figures is 123, because the next digit, 4, is below 5. Rounding 45.5147 to 4 significant figures gives 45.51 for the same reason.

Enter your number and the number of significant figures in the calculator above for the exact rounded result, in standard, e-notation or scientific format. Rounding can shift the last digit, so round once at the end rather than at each step of a longer calculation.

Sig figs in calculations#

Two different rules govern how many significant figures a calculated answer should keep, and you pick the rule by the operation.

Multiplication and division#

The answer takes the figure count of the input with the fewest significant figures. Multiply 2.3 (2 figures) by 3.456 (4 figures) and the exact product 7.9488 is reported as 7.9, rounded to 2 figures. Dividing 12.0 (3 figures) by 7.0 (2 figures) gives 1.7, not 1.714.

Addition and subtraction#

Here you count decimal places, not significant figures, and the answer keeps the fewest decimal places of any input. Adding 12.11 (2 decimal places) and 1.013 (3 decimal places) gives an exact 13.123, reported as 13.12. The least precise input sets the limit.

Chained calculations#

Carry extra digits through the middle of a multi-step calculation and round only the final answer. Rounding at every step lets small shifts accumulate and can move the last figure of the result.

Reading zeros correctly#

Zeros are the only digits whose significance depends on position. Leading zeros, as in 0.0072, are placeholders and never count, so that number has 2 figures. Captive zeros between non-zero digits always count, so 70.05 has 4. Trailing zeros count only with a decimal point present, so 250 is ambiguous while 250.0 has 4.

Significant figures FAQ#

How many significant figures does 0.00204 have?#

Three. The two leading zeros are placeholders and do not count, so the significant digits are 2, the captive 0, and 4. By contrast 100.20 has 5 figures, because the decimal point makes its trailing zero count too.

How many significant figures should a product keep?#

As many as the least precise factor. If you multiply a 2-figure number by a 4-figure number, round the result to 2 figures. The same rule applies to division.

How do significant figures work for addition?#

Addition and subtraction use decimal places, not figure counts. The sum keeps the fewest decimal places among the numbers added, so 12.11 + 1.013 is reported as 13.12 even though 1.013 has more figures on its own.

Do exact numbers limit significant figures?#

No. Counted quantities and defined conversions, such as 60 seconds in a minute or 1 inch = 2.54 cm, are treated as having unlimited significant figures. Only your measured values cap the precision of the answer.

How do you round a price to significant figures?#

Compute the exact value first, then round. A $15 item with 6.25% tax adds 0.9375, giving 15.9375; to the cent that is $15.94. Currency is normally rounded to a fixed two decimal places rather than to a figure count.