Download Uncertainty in Measurement

Uncertainty in
Measurement
Accuracy vs. Precision
Uncertainty



Basis for significant figures
All measurements are uncertain to some
degree
The last estimated digit represents the
uncertainty in the measurement
Each Person may estimate a
measurement differently
Person 1
6.63mls
Person 2
6.64mls
Person 3
6.65 mls
Rules for Counting Significant
Figures
1. Non-zeros always count as
significant figures:
3456 has
4 significant figures
Rules for Counting Significant
Figures
2. Leading zeroes do not count as
significant figures:
0.0486 has
3 significant figures
Rules for Counting Significant
Figures
3. Captive zeroes always count as
significant figures:
16.07 has
4 significant figures
Rules for Counting Significant
Figures
4. Trailing zeros (or zeros after a non-zero
digit) are significant only if the number
contains a written decimal point:
9.300 has
4 significant figures
100 has
1 significant figure
100. has
3 significant figures
Sig Fig Practice #1
How many significant figures in the following?
1.0070 m  5 sig figs
17.10 kg  4 sig figs
100,890 L  5 sig figs
3.29 x 103 s  3 sig figs
0.0054 cm  2 sig figs
3,200,000 mL  2 sig figs
These all come
from some
measurements
Rules for Significant Figures in
Mathematical Operations

Addition and Subtraction: The number
of decimal places in the result equals the
number of decimal places in the least
precise measurement.
 6.8
+ 11.934 =
 18.734  18.7 (3 sig figs)
Rules for Significant Figures in
Mathematical Operations

Multiplication and Division: # sig figs in
the result equals the number in the least
precise measurement used in the
calculation.
 6.38
x 2.0 =
 12.76  13 (2 sig figs)
Precision vs. Accuracy

Precision- how repeatable
Precision is determined by the uncertainty in the
instrument used to take a measurement.
 So . . . The precision of a measurement is also how
many decimal places that can be recorded for a
measurement.
 1.476 grams has more precision than 1.5 grams.


Accuracy- how correct - closeness to true value.
Measurement Errors


Random error - equal chance of being high
or low- addressed by averaging measurements
- expected
Systematic error- same direction each time
Want to avoid this
 Bad equipment or bad technique.




Better precision implies better accuracy
You can have precision without accuracy
You can’t have accuracy without precision
(unless you’re really lucky).
Percent Error


Percent Error compares a measured value to its
true value.
It measures the accuracy in your measurement.
%Error = Measured value – accepted value x 100
accepted value
Average Deviation

Average Deviation – measures the repeatability
(or precision) of your measurements.

Deviation = measured value – average value
You calculate the deviation for each
measurement and then take the average of those
deviations to get the “Average Deviation”
Measurement is then reported as the
average + average deviation
For example: 6.64mls + 0.01mls









Each Person may estimate a measurement
differently
Deviation
Person 1
6.63mls
0.01 mls
Person 2
6.64mls
0.00 mls
Person 3
6.65 mls
0.01 mls
Average
6.64 mls +/- 0.01 mls