Converting between absolute and relative uncertainty

[faisal]

how do i find the absalute uncertainty for the following
82.5+/-5.2%
679800+/-0.19%
0.0079+/-8.1%
420+/-23%
calculate the relative uncertainty for the following
1. 2.75 0.06
2. 714 8
3. .0031 0.0008
4. 204000 5000
5. 1.78 x 10-3 6 x 10-5
my answers
1. 2%
2. 1.12%
3. 2.5%
4. 2.4%
5. 3.4%

 

[OlderDan]

how do i find the absalute uncertainty for the following
82.5+/-5.2%
679800+/-0.19%
0.0079+/-8.1%
420+/-23%
calculate the relative uncertainty for the following
1. 2.75 0.06
2. 714 8
3. .0031 0.0008
4. 204000 5000
5. 1.78 x 10-3 6 x 10-5
my answers
1. 2%
2. 1.12%
3. 2.5%
4. 2.4%
5. 3.4%

I assume there is a ± between the numbers in the second set of 5. #3 is incorrect. For #1, I would think you might keep another decimal place or two as you did for the others.

Finding absolute uncertainty from % uncertainty is the reverse process that you used for finding % from absolute. What is 5.2% of 82.5?

 

[thepatientmental]

Absolute uncertainty is the measure of the range of values that a measurement could potentially have, while relative uncertainty is the ratio of the absolute uncertainty to the measured value. To find the absolute uncertainty, you need to multiply the given percentage uncertainty by the measured value.

For the first set of values, the absolute uncertainty would be:
1. 82.5 x 5.2/100 = 4.29
2. 679800 x 0.19/100 = 1291.62
3. 0.0079 x 8.1/100 = 0.0006399
4. 420 x 23/100 = 96.6

To find the relative uncertainty, you need to divide the absolute uncertainty by the measured value and multiply by 100 to get a percentage.

For the second set of values, the relative uncertainty would be:
1. (0.06/2.75) x 100 = 2.18%
2. (8/714) x 100 = 1.12%
3. (0.0008/0.0031) x 100 = 25.81%
4. (5000/204000) x 100 = 2.45%
5. (6 x 10^-5 / 1.78 x 10^-3) x 100 = 3.37%