A Perfectionist's Worst Nightmare

Perfectionists would cringe if they heard this unfortunate fact: NO MEASUREMENT IS EXACT.  You can always divide a measurement into smaller pieces.  1m = 1000000000 nm.  So, the only thing that's exact are quantities which you can count. 


1 banana



2 apples



3 cupcakes

Absolute Uncertainty
The last digit of a measurement is just an estimate, and absolute uncertainty is about looking at the amount of error a measurement could have. 

Method 1:
Discard data that doesn't fit.  Calculate the average measurement. Then find the largest difference between the data and the average measurement. That (+) is the absolute uncertainty.

E.g.
5 students measure the length of a classroom with metre sticks.  Here is the data they collected.  Find the absolute uncertainty. 

Student	Measurement
1	10.236 m
2	10.280 m
3	10.201 m
4	10.102 m
5	10.258 m

1)     Cancel out student #4's measurement because it doesn't come close to the other students.
2)     Find the mean measurement. [10.236+ 10.280 + 10.201 + 10.258 = 40.975/4 = 10.243 m]
3)     Largest measurement - average = 0.037
4)     Smallest measurement - average = -0.042
5)     Absolute uncertainty = 10.243 + 0.042 m.

Method 2:
Every measuring instrument has some degree of uncertainty.  A ruler can only measure to mm.  Since we always use 0.1 of the smallest measurement, we would state the absolute uncertainty as +0.001 m.

Relative Uncertainty
Relative uncertainty is a ratio of the absolute uncertainty/estimated measurement.  It is stated in %. The greater the quantity and the less absolute uncertainty, the more precise a measurement is. 

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