# Accuracy of the Difference

## Main Question or Discussion Point

Me and some colleagues discussed accuracy of measurements. We didn't agree on how to treat the accuracy if two values are used to find the value, i.e. the difference between two values.

Situation (explanation)
The weight of a mass m of approximately 5 μg is to be scaled. The scale has an error e. How would you treat the error in this measurement if the scaling is done as such. 1 m is scaled in a ≈2 g container. 2 the ≈2g is scaled without m. 3 the difference is between measurements 1 and 2 is used to find m.

What is the error in this measurement?

Cheers!

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.Scott
Homework Helper
First, the term for that ≈2g is tare.
What you have not specified is the error: e.

In general, the accuracy of a scale is specified by a weight.
For example, if e=10μg, then you will not be able to weight your 5μg mass.
If e=1μg, then you should be able to measure your mass to within 1ug. But since two measurements are made it is possible to have a worse-case situation where the error is 2μg.

Sometimes e is specified as a percentage.
So if e = 0.1%, you will not be able to measure 5μg with 2g of tare.
If e = 0.0001%, you will be able to measure 5μg with 2g of tare to within 2μg.

Hi, thanks for the input! Sorry if the example wasn't well thought out...

I found some data sheets for the scales. It seems it is accustom to present the error e as linear, thus the measurements for m can be presented as Δm±e, not Δm±2e as if the error is random, or Δm as if the error is constant.

Me and some colleagues discussed accuracy of measurements. We didn't agree on how to treat the accuracy if two values are used to find the value, i.e. the difference between two values.
The error in the difference of two values is treated the same as the error in the sum of two values. Just think of the difference as adding a negative value with the same error.

The error in the difference of two values is treated the same as the error in the sum of two values. Just think of the difference as adding a negative value with the same error.
Yes Sir i agree
And then if you need relative error then divide in the end

By the way you can also use the magic formula with partial differentials to get to error.