# Absolute & relative uncertainty

• faisal
What is 0.19% of 679,800? etc. You can do those calculations. That gives you the absolute uncertainties.Finding relative uncertainty is finding the uncertainty as a percentage of the actual measured value. For example, for the first one, you would divide 0.06 by 2.75 and multiply by 100. So the answer is 2.18%. You can do the same for the others. In summary, to find absolute uncertainty from % uncertainty, find the % of the given values. To find relative uncertainty, divide the given uncertainty by the actual value and multiply by 100.
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
1. 2%
2. 1.12%
3. 2.5%
4. 2.4%
5. 3.4%

faisal said:
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
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?

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%

## What is absolute uncertainty?

Absolute uncertainty is a measure of the range of possible values for a given measurement. It is typically expressed as a plus or minus value, and represents the maximum possible difference between the measured value and the true value.

## What is relative uncertainty?

Relative uncertainty is a measure of the uncertainty of a measurement relative to the size of the measurement itself. It is typically expressed as a percentage or decimal value, and is calculated by dividing the absolute uncertainty by the measured value.

## How is absolute uncertainty calculated?

Absolute uncertainty is typically calculated by taking the difference between the highest and lowest possible values for a measurement. This range is then divided by two to get the absolute uncertainty value.

## How is relative uncertainty calculated?

Relative uncertainty is calculated by dividing the absolute uncertainty by the measured value and multiplying by 100 to get a percentage. Alternatively, it can be expressed as a decimal by dividing the absolute uncertainty by the measured value.

## Why is it important to consider both absolute and relative uncertainty?

Absolute and relative uncertainty are both important in understanding the accuracy and precision of a measurement. Absolute uncertainty tells us the range of possible values, while relative uncertainty gives us a measure of how significant that range is in relation to the measured value. Both are necessary for a complete understanding of the uncertainty of a measurement.

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