Many math and science teachers require students to use the correct significant figures when making calculations, taking measurements, and reporting data. In order to have accurate results, the significant figures must be correct. Remember, your data is only as accurate as your least accurate measurement (think of “the weakest link”). Here are a few other rules to keep in mind:
Rule 1: All NON-ZERO numbers (1,2,3,4,5,6,7,8,9) are always significant.
48,932 = 5 sig figs
123.4 = 4 sig figs
Rule 2: All zeroes BETWEEN non-zero numbers are always significant.
900.06 = 5 sig figs
102.096 = 6 sig figs
Rule 3: All zeroes which are simultaneously to the RIGHT of the decimal point and at the END of the number are always significant.
45.900 = 5 sig figs
10.0 = 3 sig figs (10 = 1 sig fig)
Rule 4: All zeroes which are to the LEFT of a written decimal point and are in a number GREATER than ONE are always significant.
10. = 2 sig figs
120. = 3 sig figs (120 = 2 sig figs)
Therefore, all zeroes which are to the RIGHT of a written decimal point and are in a number LESS than 1 are always INSIGNIFICANT.
0.0004 = 1 sig fig
0.0030 = 2 sig figs (combination of Rules 3 & 4)
Rule 5: For ADDITION and SUBTRACTION, the LEAST number of significant figures in the DECIMAL portion only determines the answer.
19.28 g + 29.1 g + 82.132 g = 130.5 g (rounded from 130.512)
304 mL – 298.5 mL = 5 mL (rounded from 5.5)
Rule 6: For MULTIPLICATION and DIVISION, the LEAST number of significant figures in the PROBLEM, determines the significant figures in the answer.
11.21 km x 4.3 km = 5.2 km^2 (rounded from 5.203)
12.5 m / 0.13 s = 96 m/s (rounded from 96.15384615)