It is computed as:. The percent uncertainty can be interpreted as describing the uncertainty that would result if the measured value had been units. A similar quantity is the relative uncertainty or fractional uncertainty. It is simpler to compute and is given by:.
The relative uncertainty can be interpreted as describing the uncertainty that would result if the measured value had been just one unit. With these two new representations for uncertainty, we must be careful in speech and writing so that our audience is clear about which one is being used.
For example: suppose measurements of the length of two pieces of string are made, with the goal of knowing their combined length. The 1 cm uncertainty on each measurement added to give a combined uncertainty of 2 cm. The above simple example dealt with what we call absolute uncertainty. Another way to express uncertainty is the percent uncertainty. For example, the percent uncertainty from the above example would be and.
In some cases of error propagation the uncertainties are used and in other cases, the percent uncertainties are used. The rules for determining which to use are given below:.
When two measurements with associated absolute uncertainties are added or subtracted, the overall absolute uncertainty is equal to the sum of their absolute uncertainties. When two measurements with associated percent uncertainties are multiplied or divided, the overall percent uncertainty is equal to the sum of their percent uncertainty.
The area and perimeter of a rectangular table are to be calculated. The table is measured to be Because the perimeter is found by adding the sides, rule 1 is used:. The perimeter is. The area of the table is calculated to be significant digits are underlined. Since , we write the area in a variety of ways:. The reason some digits are called insignificant is that they are insignificant:.
All of these round to , giving. Within the percent error formula the experimental value is your calculated value, and the accepted value is your known or true value. Zero error can contain as many errors as you wish until the error occurs. This is not abstract as it seems.
Uncertainty on the other hand can't contain any information of this sort as zero errors. If you can't tell exactly then, especially in non-linear systems, you have logical problem of sorting out errors. The percent difference is the absolute value of the difference over the mean times Asked by: Zoheir Isberner asked in category: General Last Updated: 9th January, What is the difference between uncertainty and percent error?
Percent error is used when comparing an experimental result E with a theoretical value T that is accepted as the "correct" value. Often, fractional or relative uncertainty is used to quantitatively express the precision of a measurement.
How many significant figures do you need for Percent uncertainty? What is the uncertainty of a ruler? Thus, a Ruler A can give the measurements 2. What do you mean by uncertainty? Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown.
What is the formula for calculating uncertainty? To begin, simply square the value of each uncertainty source. Next, add them all together to calculate the sum i.
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