Identifying and eliminating systematic errors is important for increasing accuracy. They can be reduced by using better equipment or improving practical technique.
Accuracy
Accuracy is how correctly a piece of apparatus measures regardless of precision. If a car is travelling at 55 kph and a police speed detector reads 55kph, it is accurate. If it reads 48 kph or 65 kph it is inaccurate. There is something wrong with the equipment.
Example
The temperature is 20.0OC. Some students obtained the following results when they measured the temperature.
Determining Uncertainties in Calculated Results
Uncertainties can be quoted in absolute or percentage terms.
- Absolute uncertainty = Measurement ± Uncertainty
Absolute Uncertainty
-
Percentage uncertainty = ______________________ x 100
Measurement
Mass
- 1. Consider weighing 1.00g of solid. If you use a two decimal place balance, the mass recorded will be to the nearest 0.01g.
- The absolute uncertainty is 1.00g ± 0.01g
0.01
-
The percentage error is _____ x 100 = 1%
1.00
2. Consider weighing the same mass of solid on a three decimal place balance. The mass recorded will be to the nearest 0.001g.
- The absolute uncertainty is 1.00g ± 0.001g
0.001
-
The percentage error is _____ x 100 = 0.1%
1.000
3. Consider weighing 10g of solid on a three decimal place balance.
- The absolute uncertainty is 10.000g ± 0.001 g
0.001
-
The percentage error is _______ x 100 = 0.01%
10.000
Volume
4. Consider measuring 25cm3 in a 25cm3 measuring cylinder. The measurement will normally be to the nearest 0.5cm3, so in this case
-
The absolute uncertainty is 25.0 cm3 ± 0.5cm3
0.5
-
The percentage error is _____ x 100 = 2.0%
25.0
This is a much larger error than normally occurs when measuring mass. Other equipment has lower percentage errors.
5. If you use a transfer pipette or a standard / volumetric flask, the accuracy is quoted on the apparatus itself, but is normally 0.25% or 0.125%. However, they are appropriate only for specific volumes.
6. If you use a graduated pipette, as with all measuring equipment, specify a capacity closest to the target volume. For example, if you want to measure 22 cm3 of liquid using a 25 cm3 graduated pipette, the reading will usually be to the nearest 0.2cm3.
-
The absolute uncertainty is 22.00 cm3 ± 0.2cm3
0.2
-
The percentage error is _____ x 100 = 0.9%
22.0
7. A burette is more accurate still, and you can obtain readings to the nearest 0.05cm3. However there are two uncertainties in the measurement because an initial and a final reading are taken. If 25cm3 is measured, the % error would be:
0.05
-
_______ x 2 x 100 = 0.4%
25.00
Used well, the burette is very accurate. However the uncertainty increases dramatically for smaller volumes.
Time
10. Finally, consider a reaction time of 100s measured on a digital stopwatch. These often show times to the nearest 0.01s. The % error would be:
- The absolute uncertainty is 100.00 s ± 0.01s
0.01
-
The percentage error is _____ x 100 = 0.01%
100.0
This is wonderful, but how quickly can you stop and start it? The error is really more like 0.2%, and operator incompetence becomes important.
Propagating Uncertainty in Equations
The overall percentage uncertainty is the sum of all the percentage uncertainties obtained for the different measurements.
