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Mathematical Operations with Significant Figures • When completing math calculations, the final answer must be reported rounded to the appropriate number of significant figures. • The answer is rounded according to the LAST mathematical operation completed. Rules • 1. Complete calculations following the order of operations. • 2. If the FINAL step is MULTIPLICATION or DIVISION: – A. Look at each value given in the problem and find the one with the LEAST number of significant figures. – B. Round the FINAL ANSWER to the same number of significant figures. – DO NOT ROUND UNTIL THE FINAL STEP! Mult/Div Examples • 4.59 X 1.22 = 5.5998 (3 sf) (3 sf) =5.5998 = =5.60 (3sf) • • • • • 45.6 0.002454 (3 SF) (4 SF) = 18581.90709 = 18581.90709 = 18600 or convert to scientific notation and round = 1.86 x 104 • ADD/SUBTRACT • Complete calculations following order of operations. • If the FINAL step is addition or subtraction: – A. Only consider SF to the RIGHT of the decimal. – B. Determine the FEWEST SF to the right of the decimal. – C. Round FINAL ANSWER to this number of significant figures. ADD/SUBTRACT EXAMPLES 25.4 63.66 + 102.44 191.50 = 191.50 = 191.5 (1SF) (2 SF) (2 SF) • 15.000 – 2.3791 = 12.6209 • (3 sf) • = 12.6209 (4 sf) = 12.621