Quick Answer

The number 0.004050 has four significant figures. The leading zeros are not significant, but the zero between 4 and 5 and the trailing zero after 5 are both significant.

Count Significant Figures

Number

Enter as a string to preserve trailing zeros (e.g., 4.50)

Round to Significant Figures

Number

Significant Figures

Common Examples

Input	Result
0.00320	3 significant figures
100	1 significant figure
100.	3 significant figures
45.0060	6 significant figures
Round 0.08742 to 2 sig figs	0.087

How It Works

The Rules

Significant figures reflect the precision of a measurement. The standard rules for identifying significant digits are:

Rule 1: Non-zero digits are always significant. In the number 7,284, all four digits are significant.

Rule 2: Zeros between non-zero digits (captive zeros) are significant. In 1,003, all four digits are significant because the two zeros are trapped between 1 and 3.

Rule 3: Leading zeros are never significant. They serve only to position the decimal point. In 0.0045, only the 4 and 5 are significant (2 sig figs).

Rule 4: Trailing zeros after a decimal point are significant. In 2.500, all four digits are significant. The trailing zeros indicate that the measurement is precise to the thousandths place.

Rule 5: Trailing zeros in a whole number without a decimal point are ambiguous. By common convention, they are not considered significant. The number 1200 has 2 significant figures. Writing it as 1200. (with a decimal point) indicates 4 significant figures.

Rounding to Significant Figures

To round a number to n significant figures:

1. Start from the leftmost non-zero digit.
2. Count n digits to the right.
3. Look at the next digit. If it is 5 or greater, round the last counted digit up. Otherwise, leave it as is.
4. Replace remaining digits to the right with zeros (or drop them if they are after a decimal point).

Worked Example

How many significant figures does 0.004050 have? The leading zeros (0.00) are not significant (Rule 3). The digit 4 is significant (Rule 1). The zero between 4 and 5 is significant (Rule 2). The digit 5 is significant (Rule 1). The trailing zero after 5 is significant because it follows the decimal point (Rule 4). Total: 4 significant figures.

To round 86,372 to 3 significant figures: the first three significant digits are 8, 6, 3. The next digit is 7, which is 5 or greater, so round up. Result: 86,400.

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Frequently Asked Questions

Why are significant figures important?

Significant figures communicate the precision of a measurement. Reporting a length as 3.50 m (three sig figs) tells the reader the measurement is precise to the nearest centimeter, while 3.5 m (two sig figs) indicates precision only to the nearest tenth of a meter. Using the correct number of sig figs prevents overstating the accuracy of calculated results.

Are trailing zeros significant in a whole number?

Trailing zeros in a whole number without a decimal point are ambiguous. By convention, 1500 is usually treated as having 2 significant figures. To indicate that the trailing zeros are significant, write the number with a decimal point (1500.) or use scientific notation (1.500 x 10^3 for 4 sig figs).

How do significant figures work in calculations?

For multiplication and division, the result should have the same number of significant figures as the input with the fewest sig figs. For addition and subtraction, the result should have the same number of decimal places as the input with the fewest decimal places.

Does the number zero have any significant figures?

A standalone zero (0) has one significant figure. When zeros appear as leading digits (as in 0.005), those leading zeros are not significant. The significance of zeros depends entirely on their position relative to non-zero digits and the decimal point.