The uncertainty of a measured value can also be presented as a percent or as a simple ratio.(the relative uncertainty). THe percent uncertainty is familiar. It is computed as:

A similar quantity is the relative uncertainty (or fractional uncertainty). It is simpler to compute and is given by:

With these two new representations for uncertainty, we must be carefull in speech and writing so that our audience is clear about which one is being used. The following list describes accepted usage.

• Absolute uncertainty: This is the simple uncertainty in the value itself as we have discussed it up to now. It is the term used when we need to distinguish this uncertainty from relative or percent uncertainties. If there is no chance of confusion we may still simply say "uncertainty" when refering to the absolute uncertainty. Absolute uncertainty has the same units as the value. Thus it is: 3.8 cm0.1 cm.
• Relative Uncertainty: This is the simple ratio of uncertainty to the value reported. As a ratio of similar quantities, the relative uncertainty has no units. In fact there is no special symbol or notation for the relative uncertainty, so you must make it quite claer when you are reporting relative uncertainty. 2.95 kg 0.043 (relative uncertainty)
• Percent Uncertainty: This is the just the relative uncertainty multiplied by 100. Since the percent uncertainty is also a ratio of similar quantities, it also has no units. Fortunatly there is a special notation for the percent uncertainty (%), so it will be easily recognized in writing. 2.95 kg 4.3%

Note that it is acceptable to report relative and percent uncertainties to two figures. THis is to prevent rounding errors when we convert back to absolute uncertainty.

The percentage uncertainty is of great importance in comparing the relative accuracy of different measurements. For example, if we limit ourselves to 0.1 percent accuracy we know the length of a meter stick to 1 mm, of a bridge 1000 meters long to 1 meter, and the distance to the sun (93 million miles) to no better than 93,000 miles. Thus in giving the result of a measurement, one should carry enough figures to show the accuracy of the measurement, no more and no less , and should in addition state the A.D. or the percentage uncertainty. For the three examples given above one should write:

1. 1.0000.001 meters (or 1.000 meters0.l%)
2. 10001 meter (or 1000 meters0.1%)
3. (93.000.09) x 10⁶ miles (or 93.00 x 10⁶ miles0.1%)

• Determine the relative uncertainty for each of the measurements below. Type your answer in the text box, then click on the bar in the last column for the correct answer.

1. 2.750.06		Answer Relative: 0.022 Percent: 2.2%
2. 7148		Answer Relative: 0.011 Percent: 1.1%
3. .00310.0008		Answer Relative: 0.26 Percent: 26%
4. 2040005000		Answer Relative: 0.025 Percent: 2.5%
5. 1.78 x 10-36 x 10-5		Answer Relative: 0.034 Percent: 3.4%

• Determine the absolute uncertainty for each of the measurements below. Round your results where needed to show the proper number of significant figures. Type your answer in the text box, then click on the bar in the last column for the correct answer.

6. 3.790.73%		Answer 3.79 +/- 0.03
7. 82.55.2%		Answer 82 +/- 4 The five rounds down.
8. 6798000.19%		Answer 680000 +/- 1000 There are really three significant digits here. Scientific Notation would be better.
9. 0.00798.1%		Answer 0.0079 +/- .0006
10. 42023%		Answer 400 +/- 100