Every measurement has UNITS Every measurement has UNCERTAINTY 2 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 ID: 283237
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Slide1
1
Measurements:
Every measurement has UNITS.
Every measurement has UNCERTAINTY.Slide2
2
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. Slide3
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 cm2.10 cm2.100 cmSlide4
4
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 measurement
the digit farthest to the right is considered to be estimated.
0
1
2
1.
3
2.
0Slide5
5
Sig. Fig. Rules (with measurements):
1. All
non-zero digits are significant.
3 sig figs
1222 4 sig figs
0.54 2 sig figs
2. Zeros
at the beginning
of a measurement are not significant.
0.005 1 sig fig0.0015 2 sig figs
0.00000887 3 sig figsSlide6
6
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 figs
74.00 4 sig figs 105.20 5 sig figs
0.0050 2sig figs 2.000 4 sig figs 20.0 3 sig figsSlide7
7
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 placeSlide8
8
Measurement Calculations with scientific notation.
Addition/subtraction: must be placed into the same notation.
(2.3 x 10
3
) + (3.2 x 10
4
) =
0.23 x 10
4
+3.2 x 104
3.43 x 104
= 3.4 x 10
4Slide9
9
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.
1
1
5.5740539 cm
3
written as 120 cm
3
2 s.f.’sSlide10
10
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”Slide11
11
3. The number of significant figures in 6.0700 x 10
-4… is a. 3. b. 4. c. 5. d. 6. e. 7.
c. 5.
4. How many significant figures are there in the value 0.003060?
a. 7
b. 6
c. 5
d. 4
e. 3
d. 4Slide12
Percent Error
Indicates accuracy of a measurement
your value
accepted valueSlide13
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.
% error = 2.9 %