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V.
TREATMENT OF DATA IN CALCULATIONS
When numbers obtained from measurements
are used in calculations, care should be exercised to
avoid reporting more
significant figures in an answer than are justified by the numbers
used to obtain the answer.
Uncertainties in measurements are discussed
in your textbook. A brief summary of a few
significant features is given here.
First, we must distinguish two statistical
terms, precision and accuracy.
Precision is a measure of
how closely repeated measurements agree
with each other.
Accuracy is a measure
of how closely the final result agrees with the true or accepted value.
One
may be very precise but not very accurate,
so both precision and accuracy need to be considered in
recording data.
The precision with which some laboratory
measurements can be made is shown below:
Instrument
Precision
analytical balance
±0.003
g
10 mL graduated cylinder
±0.05
mL
50 mL graduated cylinder
±0.2
mL
100 mL graduated cylinder
±0.5
mL
buret
±0.04
mL
110°C thermometer
±0.2
°C
A.
Propagation of Errors
The error in a sum or difference is considered
to be the sum of the errors in the individual
terms.
The relative
error in a product or quotient is considered to be the sum
of the relative errors in the
numbers multiplied or divided.
Example:
initial volume of H2O
6.90 mL ± 0.05 mL
final volume of H2O
4.65 mL ± 0.05 mL
change in volume
2.25 mL ± 0.10 mL
