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Propagated and Relative Error

Propagated and Relative Error. Propagated Error. First identify a formula that represents the situation given. Make sure your formula is written in terms of the variables that are being measured.

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Propagated and Relative Error

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  1. Propagated and Relative Error

  2. Propagated Error • First identify a formula that represents the situation given. • Make sure your formula is written in terms of the variables that are being measured. • If you have two variables, like length and width you can assume that the same error in measurement that you have for the length will be the same as the width (same person measuring with same instrument, error should be consistent) • Create the differential of the formula. Don’t forget you dx part (change). • The dx part will end up being the error when you plug things in. • Propagated error is a +- value, you accuracy in measuring could have error in terms of over measuring or under measuring. So we will always throw in a +-.

  3. The radius of a ball is measured to be 3.2 inches. If the measurement is correct to within 0.03 inches, estimate the propagated error in the volume (V) of the ball.

  4. A rectangle has a length of 18 inches and a width of 12 inches, find the propagated error if the measurements are within 1/8 of a inch correct. What is the relative error? • Relative Error is the ratio of the propagated error to the actual theoretical value. • If talking about volume it would be dV/V • Area would be dA/A

  5. The volume of a sphere is calculated. If the diameter is 12 cm and the measurement is within 0.01 cm accurate what is the propagated and relative errors?

  6. Homework • Pg. 240 27-31

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