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Uncertainties and Error Propagation

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I have attached 5 questions involving +/- error analysis involving addition, subtraction, and multiplication/division.

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Uncertainties and Error Propagation

Useful links:
http://www.youtube.com/watch?v=6XZsfV5FCwc (forward to about 13 minutes)

Addition and Subtraction
The simpler method in determining the uncertainty of measurements that are added or subtracted would be to add the absolute value of the uncertainty of each measurement.
1st measurement: x  x
2nd measurement: y  y

z = x + y OR z = x - y
z = |x| + |y|
Final answer = z  z

Multiplication and Division
The ratio of the uncertainty of a product divided by the product is equal to the sum of the ratios of the uncertainty of each factor divided by the factor. To get the uncertainty, you have to multiply the resulting ratio with the product. The same rule applies to quotients.

z = xy or z = x/y

Final answer = z  z

1. (245  23) - (222)
245 - 22 = 223
z = |23| + |2| = 25
Final answer = 223  25

Proceed with the division first:
100.3 / 22.1 = 4.54 (round off to 3 significant figures because of 22.1)
For the quotient:

(Each addition term is rounded off to 1 significant figure because of 0.4, and the ...

Solution Summary

This document shows how to calculate the errors or uncertainties of measurements involved in addition, subtraction, multiplication, division or a combination of these. There is also a problem regarding how to calculate for the error in a molarity given buret readings for volume.

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Propagation of Uncertainties

A) According to theory, the period T of a simple pendulum is T=2Π√(L/g), where L is the length of the pendulum. If L is measured as L=1.40 +/- 0.01 m, what is the predicated value of T?
b) Would you say that a measured value of T=2.39 +/- 0.01 s is consistent with the theoretical prediction of part (a)?

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