significant figures

Figures in a number that, by virtue of their position, express the magnitude of that number to a specified degree of accuracy. In a number, the first significant figure is the first figure that is not a 0. The final significant figure is rounded up if the following digit is greater than 5. For example, 5,463,254 to three significant figures is 5,460,000; 3.462891 to four significant figures is 3.463; 0.00347 to two significant figures is 0.0035.

To round to one significant figure, first the significant figure must be found, then the figure following the significant figure must be checked; if the figure following the significant figure is a 5, 6, 7, 8, or 9, then 1 should be added to the significant figure. For example, in the number 31.4, the first significant figure is 3 and the following figure is 1, so 31.4 rounded to one significant figure is 30. Using the same method, 214 becomes 200, 58.8 becomes 60, and 0.72 becomes 0.7.

When rounding to any significant figure, the figure after the final significant figure should be checked to determine if the final significant figure should be rounded up. For example:

432 to two significant figures is 430 (no need to round up)

43,762 to three significant figures is 43,800 (round up)

0.07036 to three significant figures is 0.0704 (round up; note that the 0 in the middle of the number is counted as significant, whereas the 0s before the 7 are ignored).