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Mathematical Operations with Significant Figures

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.

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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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