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Significant Figures: Rules for What Digits Count as Significant (*note—for measurements only) **NOTE: Exact numbers obtained from counting, numerical definitions or equivalents (60 seconds = 1 hour, 1kg = 1,000g, 10 eggs) are considered to have infinite significant figures.** Number Digits to Count Example Significant Figures No zeros All digits 13534 5 Leading Zeros (to the left) Captive Zeros None of the zeros, All non-zeros digits All digits 0.00045 2 12004 5 Trailing Zeros (to the right) Count all non-zero digits 400.0 and 400 and 400. and trailing zeros WHEN and 0.040 DECIMAL PRESENT. Do not count if no decimal point All digits in front of x10 3.710 x 107 2.040 x 10-2 Scientific Notation 4 and 1 and 3 and 2 3 4 (from 0.02040) Rules for Use of Significant Figures in Calculations In multiplication and division: answers must be the same as the least number of significant figures used in the calculation. Example: 234.75 grams x 24.1 grams Note the first number has 5 sig figs and the second number has 3 sig figs. The answer must be the same as the least number of sig figs used in the calculation (3). the raw calculation shows 5,657.475 grams (not correct for sig figs) Correct Answer: 5,660 grams (rounding to three, correct sig figs ) In addition and subtraction: answers must be the same as the least number of decimal places regardless of the total number of significant figures of each number. Example: 41.273 + 10,034.2 Note the first number has 3 digits after the decimal point, the second number has 1 number after the decimal point. Following the rules, the answer must be the same as the least number of decimal places after the decimal point. Correct Answer: 10,075.5 (10,075.473 rounded up to one place after the decimal)