Chapter 5 - Measurements and Calculations
Calculations with Sig Figs
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
Addition and Subtraction
Align the decimal points and carry out the calculation. First column from the left with 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
Scientific Notation and Multiplication and Division
a. Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F.
b. 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)
Scientific Notation and Addition and Subtraction
- must be in the same power of ten and same unit before you add or subtract coefficients
- HINT: convert to larger exponent
Ex 1: 3.0 x 1023 m + 1.0 x 1022 m
Problem Solving and Dimensional Analysis
Conversion factor – ratio of two parts of the statement that relates the two units
Equivalence Statement – true statement
Dimensional Analysis – when used properly all units will cancel out except the desired unit
Ex 1:
Ex 2:
Ex 3:
Determining Error
___________________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.
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
Ex: 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.
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