How to calculate Relative Uncertainty - Measurements are in different units

[amanbhai]

can anyone help me in calculating relative uncertainty of measurement of different test whose measurements are in different units.
positively

[apestate]

amanbhai

To clarify, what are the different units in question? Are you asking about the units of linear vs. angular?

The reason I'm confused is because measurements and units should be absolute. If an angle is measured in base 60 degrees minutes seconds, or decimal degrees, the amount of uncertainty due to the conversion is a rectangular distribution of the rounding error.

Could you help us clarify?

[Jim Wynne]

Originally Posted by amanbhai

can anyone help me in calculating relative uncertainty of measurement of different test whose measurements are in different units.
positively

I'm not sure I understand the question; if measurement "A" has an uncertainty of x and measurement "B" has an uncertainty of y, it doesn't matter what the units of measure used in A and B were. The uncertainty value is what it is, regardless of the UOM.

A month or so ago I saw an AP story about how the British (tennis) Open tournament had decided on unequal prize money for men and women, this after the other Grand Slam tournaments had made the money equal for both sexes. The story said,

The All England Club announced Tuesday that the men's winner this year will receive $1.170 million and the women's champion $1.117 million, a difference of $53,000. It's a four percent increase in British currency.

Well, it's a 4% increase in drachmas or piasters or pesos, too. 4% is 4%.

[Tim Folkerts]

Typically, a "relative" measurement simply means a ration of a value to the whole. For uncertainty, this would be (uncertainty)/(measured value). For example, if the test result is 10 kg +/- 0.2 kg, the relative uncertainty would be (0.2 kg)/(10 kg) = 0.02 = 2%.

Note that the units cancel, so relative uncertainty has no units. This means the original units don't matter and it is easier to compare various measurements. As a simple example, density requires measurements of both mass and volume, which obviously have different units. If mass has a relative uncertainty of 0.1% but volume has a relative uncertainty of 2%, then improving the mass uncertainty won't really improve accuracy of the density calculation, but improving the volume uncertainty would have a bigger effect.


Tim F