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Understanding Mathematical Operations with Significant Figures

Learn how to round answers to correct significant figures after mathematical operations. Follow rules for rounding in multiplication, division, addition, and subtraction.

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Understanding Mathematical Operations with Significant Figures

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  1. Mathematical Operations with Significant Figures

  2. 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. • The least precision in the problem is the greatest precision in the answer!

  3. Rules • 1. Complete calculations following the order of operations. MULTIPLICATION/DIVISION • 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!

  4. Multiplication/Division Examples • 4.59 X 1.22 = 5.5998 = 5.5998 =5.60 • 3 sf 3sf 3sf 3sf • 3 sf 45.6 = 18581.90709 round final • 4 sf 0.002454 answer to 3 SF • = 18587.90709 3SF • = 186003Sf

  5. ADDITION/SUBTRACTION • Complete calculations following order of operations. • If the FINAL step is addition or subtraction: • A. Consider digits ONLY to the RIGHT of the decimal. • B. Determine the fewest SF to the rightof the decimal. • C. Round final answer to this number of SF.

  6. ADD/SUBTRACT EXAMPLES A. 25.4 (1 SF past decimal) 63.66 (2 SF past decimal) + 191.50(2 SF past decimal) = 191.56 (Round to 1 SF past decimal) = 191.6 Final answer rounded to 1 SF past decimal. B. 15.000 – 2.3791 = 12.6209 (3 SF) (4 SF ) (Round to 3 SF past decimal) = 12.621 Final answer rounded to 3 SF past decimal

  7. Mixed Math Calculations • If you have a combination of math operations, ROUND TO SF ACCORDING TO THE RULES FOR THE LAST OPERATION YOU COMPLETE.

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