Uncertainty/Error in
Measurment
Year 11 DP Chemistry
R. Slider
Uncertainty and Error
All experimental measurements contain some
amount of uncertainty because we are limited by
the precision of the instruments that we are
using.
Error in measurement is introduced when
instruments are calibrated incorrectly or used
incorrectly.
Random vs. Systematic
Random Uncertainties
Systematic Error
Random uncertainty comes from
fluctuations in measurements
that can be greater or less than
the actual result.
These often stem from the
limitations of the equipment
being used or limitations of the
experimenter (e.g. how
precisely you can read a scale)
These errors can never be
eliminated completely, but can
be reduced by using repeats
Systematic error always affects the
measurement in one direction
only
These are due to either flaws in an
instrument that is calibrated
incorrectly (giving readings that
are too high for example) or
from experimenter error such as
in parallax error where, for
example, the readings are
consistently too low
These are reduced by good
experimental design
Reporting Uncertainty
Analogue instruments
Digital instruments
Instruments such as
thermometers and measuring
cylinders have various divisions
Digital readouts such as
electronic balances have various
precision levels
The uncertainty of an analogue
scale is +/- half of the smallest
division
The uncertainty of a digital scale
is +/- the smallest scale division
Precision and Accuracy
• Precision refers to how close repeated
measurements are to one another (has the least
uncertainty/random errors)
• Accuracy refers to how close a value is to an
accepted (true) value. Small systematic errors
lead to accurate measurements.
Precision and Accuracy
Example: Two groups are determining the gas
constant value (8.314 J/mol K). Results are:
Group A: 8.537; 8.487; 8.598; 8.492; 8.472
(Avg=8.517)
Group B: 8.13; 7.94; 8.44; 8.54; 8.22 (Avg =8.25)
Which group is more precise?
Group A (less variation/uncertainty)
Which group is more accurate?
Group B (closer to accepted value)
Significant Figures
Significant figures (s.f.) establish the precision of a number.
The rules:
1. All non-zero numbers are ALWAYS significant (e.g. 1, 2, 3...)
2. Zeroes between 2 non-zero or 2 significant numbers are ALWAYS
significant.
3. Zeros used to locate a decimal point (placeholders) are NOT significant
4. Zeroes which are SIMULTANEOUSLY to the right of the decimal point
AND at the end of the number are ALWAYS significant
5. The last significant figure on the right is the one which is somewhat
uncertain
For operations:
• When adding/subtracting, the number of digits to the right of the decimal
is the same as the number with the fewest digits to the right
• When multiplying/dividing, the number of s.f. in the answer is the same as
the least number of s.f. in any of the original numbers.
Significant Figures Examples
Determine the number of s.f. in each of these numbers
and the rule # that led you to that conclusion.
Tabulate results.
a)48,923
b)3.967
c)900.06
d)0.0004
e)8.1000
f)501.040
g)3,000,000
h)10.0
Significant Figures Examples
Number
# Significant figures
Rule
48,923
5
1
3.967
4
1
900.06
5
1,2
0.0004
1
1,3
8.1000
5
1,4
501.040
6
1,2,4
3,000,000
unspecified
1,3
10.0
3
1,2,4
Absolute and % Uncertainty
Once you have determined the uncertainty of a
single measurement (as a ± value) you can easily
determine % uncertainty.
For example:
You determine the mass of a sample to be 24.56
±0.01g. Your absolute uncertainty is 0.01g and %
uncertainty = (o.o1÷24.56) x 100 = o.04%
Absolute and % Uncertainty
When multiple readings are combined, the
following rules apply:
1. Addition/subtraction – add the absolute
uncertainties
2. Multiplication/division – add the %
uncertainties
3. Exponents – multiply the exponent by the %
uncertainties