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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