This section deals with the difference between absolute and percentage uncertainties.
This is the actual uncertainty in a reading taken using a specific piece of apparatus. The value depends on the apparatus used.
Example: The tolerance of a 25 ml pipette
The pipette may have the tolerance written on the side as: ± 0.26 ml @ 20ºC
This means that when the pipette is used exactly as per the manufacturer's instructions at 20ºC there is an in-built inaccuracy of between + 0.26 ml and - 0.26 ml.
Some pieces of apparatus do not have an inaccuracy written on them, in which case you must make an assessment based on how accurately you believe you can measure using the apparatus. You should err on the side of caution.
Example: Reading a burette
The 50 ml burette has no tolerance value written on the side.
The smallest mark on the graduated scale is 0.1 ml. It is reasonable to assume that you can assess the measurement of the liquid level to within half of the smallest graduation, i.e. 0.05 ml. This means that each reading should be given as [your value] ± 0.05 ml.
Don't forget that when a burette is used you must take TWO readings. Each reading has an uncertainty of ± 0.05 ml, therefore the total uncertainty is 0.05 + 0.05 = ± 0.1 ml
Electronic digital measuring apparatus such as electronic balances calculate the measurement for the operator. BUT they have to electronically round up the decimal place after the last decimal on the readout.
An electronic balance that measures to 2 decimal places calculates the second decimal place according to the value of the third (unseen) decimal. If the third decimal is 5, or greater, the balance rounds up the second decimal place. If the third decimal is 4 or less then the second decimal stays the same.
Example: An electronic balance which shows 27.53 g
It is possible that the actual reading (as measured by the balance) is as low as 27.525 g, in which case it has rounded up the reading so that the last decimal is 3.
It is equally possible that the actual reading as measured by the balance is as high as 27.534 g. In this case the second decimal would appear as 3.
Hence the range of values that the balance could be reading is from 27.525 g to 27.534 g.
This uncertainty is recorded as 27.53 ± 0.005 g
In summary there are three ways that you can obtain an absolute value for an uncertainty:
- Directly from the measuring instrument
- By judgement of activity undertaken
- From the 'missing' decimal place of digital readouts
A percentage, by definition, is a value out of a potential hundred.
The percentage is calculated by taking the absolute error in a measurement and dividing by the value of the measurement itself. This is then multiplied by one hundred.
A single reading cannot have a percentage uncertainty, but a measured value such as volume, time or mass does. In other words the single reading from a burette cannot be expressed as a percentage uncertainty, while the absolute uncertainty of the volue measured bform a burette does have a percentage uncertainty.
Example: Calculate the percentage uncertainty when 24.2 ml are delivered from a burette.
The burette requires two readings, the initial reading and the final reading. The volume delivered is obtained by subtraction of the initial reading from the final reading.
There is an uncertainty of ± 0.05 in each reading, ∴ total absolute uncertainty of ± 0.1 ml
The percentage uncertainty = (0.1/24.2) x 100 = 0.41% uncertainty