How this calculator works
Significant figures record how precisely a measurement is known. Every nonzero digit counts. Zeros between nonzero digits count, and zeros after the decimal point that follow a nonzero digit also count. Leading zeros before the first nonzero digit never count, and trailing zeros in a whole number without a decimal point are ambiguous, so they are treated as place holders. Rounding to a chosen count keeps the digits that carry information and replaces the rest, writing the zeros needed to show the precision.
Formula
Count significant figures from the first nonzero digit to the last retained digit. To round, find the decimal order e of the value and round to s - 1 - e decimal places, where s is the wanted count.
Worked example
0.004567 has four significant figures: 4, 5, 6 and 7. Rounded to two significant figures it becomes 0.0046. Rounded to three it becomes 0.00457. The number 1500 has two significant figures because the trailing zeros are place holders.
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Frequently asked questions
Are trailing zeros significant?
After a decimal point they are: 1.050 has four significant figures. In a whole number with no decimal point they are ambiguous: 1500 could be two, three or four depending on the measurement, so this calculator treats them as place holders and counts two.
Why does the rounded answer show zeros the original did not?
Those zeros carry meaning. Rounding 12 to four significant figures gives 12.00, which states that the value is known to the hundredths place. Dropping them to 12 would claim only two significant figures.
How does zero count?
The number zero is a special case: its significant figures cannot be determined from the value alone, so this calculator reports one. A measured zero such as 0.00 would normally carry as many significant figures as the instrument supports, which numeric input cannot express.
Does the calculator round half up?
Yes. Ties round away from zero, matching the usual classroom rule. Banker's rounding, which sends ties to an even digit, is available in the rounding tools if a standard requires it.