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UNCERTAINTY AND LAB MEASUREMENTS ALL measurements posses some level in uncertainty in their value. When you make a measurement ( ) x , you must estimate the ABSOLUTE UNCERTAINTY ( ) Δ x in your measurement. This error in measurement is based on how well you think that you could make the measurement and may be a function of the quality of the measuring instrument, the conditions under which the measurement is made and the nature of the quantity being measured. Too often we assume that the absolute uncertainty is based solely on the resolution of the measuring instrument. There is no simple prescribed formula of how to calculate the absolute uncertainty for a measured quantity (you need to perform calculus on the equation relating the measured quantities to find the absolute uncertainty). When you report a measured quantity, you need to quote it as a measurement interval () xx ±Δ . There are rounding rules that guide you in reporting the number of significant digits is the measured value x (see previous note). The Simple Physics Lab Rule : the absolute uncertainty of a measurement is reported to only one or at most two significant figures and the measurement is then rounded to the same decimal place as its absolute uncertainty. See EXAMPLE below. RELATIVE UNCERTAINTY is a measure of the precision of the measurement. If the measurement has a high degree of precision, repeated measurements (using the same equipment and technique) will produce the same result. We calculate the relative uncertainty by dividing the absolute uncertainty of the measurement by the value of the measured quantity, Δ x x . Usually this quantity is expressed as a percent. If you quote the relative uncertainty as opposed to the absolute uncertainty, you still apply the simple physics lab rule. See EXAMPLE below.
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This note was uploaded on 07/27/2010 for the course MATH MATH 1025 taught by Professor Tanny during the Spring '09 term at York University.

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