Transcript Measurements

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.
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• 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
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
2.0
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Sig. Fig. Rules (with measurements):
1. All non-zero digits are significant.
526
1222
0.54
3 sig figs
4 sig figs
2 sig figs
2. Zeros at the beginning of a measurement are not significant.
0.005
0.0015
0.00000887
1 sig fig
2 sig figs
3 sig figs
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3. Zeros in between two significant figures are
significant
0.00505
40065
3 sig figs
5 sig figs
4. Final zeros after a decimal point are significant
1.0
74.00
105.20
0.0050
2.000
20.0
2 sig figs
4 sig figs
5 sig figs
2sig figs
4 sig figs
3 sig figs
Counted numbers and definitions (2.54 cm = 1 inch) are
considered to be exact and have no effect on the number of 6
sig. figs. reported in calculations with measurements.
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 = 115.5740539 cm3
4 s.f.
2 s.f.
5 s.f.
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.
Let’s take a “Quiz”
b. precision.
b. precision.
c. qualitative.
d. quantitative.
e. property.
2. The number of significant figures in the mass
measured as 0.010210 g is
a. 1.
b. 2.
e. 5.
c. 3.
d. 4.
e. 5.
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3. The number of significant figures in 6.0700 x 10-4… is
a. 3.
b. 4.
c. 5.
c. 5.
d. 6.
e. 7.
4. How many significant figures are there in the value
0.003060?
a. 7
b. 6
c. 5
d. 4
d. 4
e. 3
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Percent Error
• Indicates accuracy of a measurement
% error 
experimental  literature
literature
your value
accepted value
 100
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 
1.40 g/mL  1.36 g/mL
1.36 g/mL
% error = 2.9 %
 100