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Sig Figs and Mixed Operations (   + -)

Sig Figs and Mixed Operations (   + -). Remember, in math the order of operations is: Parenthesis, Exponents, Mult ./Div., Add./Subtraction ( ), ^,   , + -) You need to decide HOW TO ROUND the final answer by rounding after each operation, performed in order

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Sig Figs and Mixed Operations (   + -)

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  1. Sig Figs and Mixed Operations ( + -) • Remember, in math the order of operations is: Parenthesis, Exponents, Mult./Div., Add./Subtraction ( ), ^, , + -) • You need to decide HOW TO ROUND the final answer by rounding after each operation, performed in order • You need to round the NUMBER obtained by not rounding after each operation, since we should only round at the very end

  2. Not Rounding at all: Rounding at every step Division is performed first: 16.83/15 = 1.122 round to 2 SF = 1.1 (15 has only 2 SF) Subtraction next: 1.1 – 0.46 = 0.64 round to 1/10th’s place = 0.6 (because 1.1’s most significant digit is in the 1/10th’s place) • Division is performed first: 16.83/15 = 1.122 • Subtraction next: 1.122 – 0.46 = 0.662

  3. Now, perform the rounding operation of the final step of the ‘rounding at each step’ to the number found when ‘not rounding at all’ • round to 1/10th’s place on 0.662 • 0.662  0.7

  4. Not Rounding at all: Rounding at every step Absolute Value acts as (): |50. - 42.32|= 7.68 round to 1’s place = 8 (50.’s most sig digit is in 1’s place) Division next: 8 / 42.32 = 0.181474 round to 1 SF = 0.2 (8 has only 1 SF) Multiplication next: 0.2 x 100% = 20%  round to 1 SF = 20% (0.2 has only 1 SF) • Absolute Value acts as (): |50. - 42.32|=|7.68| = 7.68 • Division next: 7.68 / 42.32 = 0.181474 • Multiplication next: 0.181474 x 100% = 18.1474%

  5. Now, perform the rounding operation of the final step of the ‘rounding at each step’ to the number found when ‘not rounding at all’ • round to 1 SF on 18.1474% • 18.1474%  20%

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