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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). |
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