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Unformatted text preview: Error Analysis This brief discussion of error analysis will be adequate for these labs. For a thorough understanding of error analysis and for further information see John R. Taylor, An Introduction to Error Analysis , 2nd Ed. (University Science Books, 1997). 1 Motivation Error Analysis is an important tool for all quantitative sciences. Measured values are always subject to uncertainty, whether due to human or machine imperfections. A measured numbers by itself, without a value for the uncertainty, carries very little meaning as it cannot rule out any other value. For example, a measurement of 5 mm is not inconsistent with one of 20 meters if the uncertainties are large enough. It is therefore important to determine and quote the uncertainty range for every measurement in an experiment, and every relevent result. 2 Units A number is not complete without the units associated with that quanity, and often the uncertainty attached to the number. Be sure to include both for any number given. For example, for a length l l = 2 . . 2 cm (1) 3 Significant Figures The number of significant figures is the number of non-zero digits in the quantity, and number of zero digits between any two non-zero digits. For example x = 120 . 34 has 5 significant figures. All digits are assumed known except the last digit on the right. This last number contains some error. For x = 120 . 34 the last digit on the right, 4, might be uncertain to 1, giving a range for the number of x = 120 . 33 to 120 . 35. The uncertainty in this last digit is denoted x = 0 . 01, where is the lowercase greek letter delta. The quantity can be written as x x . It is important to consider the significant figures when writting a number. It is similarly wrong to write 120 . 3 . 01, since the numbers appearing after 4 are not known within the uncertainty. The number of decimal places in x should always agree with the number of decimal places in x . 4 Estimating Uncertainty Often the uncertainty in a measurement depends on the reading on a scale or meter. You must decide how well you can align the pointer or object to the scale. Some examples include Meter stick, ruler, etc If the finest division is 1mm, the uncertianty might be . 5mm or perhaps a bit smaller. Science Workshop quantities such as length, time, and angle Use your judgement as to what is the appropriate number of decimal places to use. SWS allows you to change the number of decimal places observed. Consider performing sinmple experiments to see in which demical place the measurementobserved....
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This note was uploaded on 03/25/2011 for the course PHY 102 taught by Professor Khurana during the Spring '11 term at NYU.
- Spring '11