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Calculations Notes

Calculations Notes. Multiplication and Division. Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate) Ex 1: 4.63 m x 7.5 m Ex. 2: 8.460 m 2 / 2.1 m. 3sf. 4sf. 2sf. 2sf. 34.725 m 2. 4.02857143 m. 4.0 m. 35 m 2. 6.341

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Calculations Notes

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  1. Calculations Notes

  2. Multiplication and Division Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate) Ex 1: 4.63 m x 7.5 m Ex. 2: 8.460 m2 / 2.1 m 3sf 4sf 2sf 2sf 34.725 m2 4.02857143 m 4.0 m 35 m2

  3. 6.341 .789 4.2 6.799 2.41 Addition and Subtraction Align the decimal points and carry out the calculation. First column from the leftwith an uncertain digit determines the number of sig. figs. in your answer (Chop & round at the GAP) Ex 1: 6.341 g + .789 g + 4.2 g Ex. 2: 6.799 m - 2.41 m 11.3 g 4.39 m GAP GAP 11.330 4.389

  4. Scientific Notation and Multiplication and Division Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F. Division - Divide coefficients, SUBTRACT exponents, divide units, round to proper S.F. Ex 1: (1.00 x 103 m)(3.2 x 102 m) Ex. 2: (3.00 x 104 g)/(1.0 x 102 cm3) 3.2 x 105 m2 3.0 x 102 g/cm3

  5. 3.0 .10 1 Scientific Notation and Addition and Subtraction must be in the same power of ten and same unit before you add or subtract coefficients, convert to larger exponent Ex 1: 3.0 x 1023 m + 1.0 x 1022 m 3.0 x 1023 m + .10 x 1023 m 3.1 x 1023 m GAP 3.10

  6. Element Buddies • ADD PRACTICE

  7. 2.54 cm 1 inch 1 inch 2.54 cm 100 cm 1 m 1 m 100 cm Problem Solving and Dimensional Analysis Conversion factor – ratio of two parts of the statement that relates the two units Equivalence Statement – true statement in fraction form Dimensional Analysis – when used properly all units will cancel out except the desired unit 2.54 cm = 1 inch 100 cm = 1 m or or Wanted UNIT Desired UNIT # # Given with UNITS x ________________ x ______________ = # Given UNIT # Wanted UNIT

  8. Ex. 1: 250 m = ___________ km Ex. 2: 3.54 g = ___________ mg Ex. 3: 0.542 kg = __________ mg 250 m 1 km x ___________ .25 km = 1000 m 1000 mg 3.54 g x ___________ 3540 mg = 1 g 0.542 kg 1000 g 1000 mg x ________ x __________ = 542000 mg 1 kg 1 g

  9. Determining Error accepted ___________________value - correct value based on reliable references ___________________value - value measured in the lab Error = experimental value – accepted value (Note: error can be positive or negative) You will take the ___________ value of this when you calculate percent error. experimental absolute

  10. % error = (91.1 oC – 100 oC) x 100% 100 oC Determining Percent (%) Error Percent error = absolute value of error divided by accepted value and multiplied by 100% % error = experimental value – accepted value x 100% accepted value Example: You take three temperature readings of a beaker of boiling water and record: 91.3oC, 90.9oC, and 91.1oC. Evaluate accuracy, precision, and error. No, water boils at 100oC Accurate? Precise? Yes, values are close to each other Error • Find average experimental data • Use formula (91.3oC + 90.9oC + 91.1oC)/3 = 91.1oC = 8.90 %

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