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Measurements: Every measurement has UNITS.

Every measurement has UNCERTAINTY.

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Accuracy and Precision in Measurements

Accuracy: how close a measurement is to the accepted value.

Precision: how close a series of measurements are to one another or how far out a measurement is taken.

A measurement can have high precision, but not be as accurate as a less precise one.

• Precision can also mean– The number of decimal places assigned to the

measured number (The more decimal places, the more precise the measurement)

• Ex. – 2.1 cm– 2.10 cm– 2.100 cm

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Significant Figures are used to indicate the precision of a measured number or to express the precision of a calculation with measured numbers.

In any measurementthe digit farthest to

the right is considered to be

estimated.

0 1 2

1.32.0

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Sig. Fig. Rules (with measurements):

1. All non-zero digits are significant.

526 3 sig figs1222 4 sig figs0.54 2 sig figs

2. Zeros at the beginning of a measurement are not significant.

0.005 1 sig fig0.0015 2 sig figs0.00000887 3 sig figs

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0.00505 3 sig figs40065 5 sig figs

Counted numbers and definitions (2.54 cm = 1 inch) are considered to be exact and have no effect on the number of sig. figs. reported in calculations with measurements.

3. Zeros in between two significant figures are significant

4. Final zeros after a decimal point are significant

1.0 2 sig figs74.00 4 sig figs105.20 5 sig figs0.0050 2sig figs2.000 4 sig figs20.0 3 sig figs

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Calculations with sig. Figs.

Addition and subtraction:

Look at decimal places! Answer should have the same amount of decimal

places as the measurement with the

least amount 3.63 cm 13.129 cm+123.1 cm

139.859 cm = 139.9 cm

significant to the 0.1 place

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Measurement Calculations with scientific notation.

Addition/subtraction: must be placed into the same notation.

(2.3 x 103) + (3.2 x 104) =

0.23 x 104

+3.2 x 104

3.43 x 104 = 3.4 x 104

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Calculations with Sig. figs.

Multiplication and division (measurements):

Count sig figs!!Answer should have the same amount of

sig figs as the measurement with the least amount.

2.734 cm x 5.2 cm x 8.1294 cm = 4 s.f. 2 s.f. 5 s.f.

115.5740539 cm3

written as 120 cm3

2 s.f.’s

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1. The term that is related to the reproducibility (repeatability) of a measurement is

a. accuracy.b. precision.c. qualitative.d. quantitative.e. property.

b. precision.

2. The number of significant figures in the mass measured as 0.010210 g is

a. 1.b. 2.c. 3.d. 4.e. 5.

e. 5.

Let’s take a “Quiz”

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3. The number of significant figures in 6.0700 x 10-4… isa. 3.b. 4.c. 5.d. 6.e. 7.

c. 5.

4. How many significant figures are there in the value 0.003060?

a. 7b. 6c. 5d. 4e. 3

d. 4

Percent Error

• Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

Percent Error• A student determines the density of a substance to

be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.9 %