Reading Error Of A Meter Stick
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Systematic Error Calculator
science and math community on the planet! Everyone who loves science is here! systematic error calculation Meter Stick Mar 31, 2005 #1 Haftred Can one read a meter stick down to a tenth of a millimeter? For
Fractional Error Calculator
example, could I reasonably measure an object as 32.43 cm using a meter stick? Haftred, Mar 31, 2005 Phys.org - latest science and technology news stories on Phys.org •The quantum sniffer dog error definition in physics •Light-driven atomic rotations excite magnetic waves •Clearing 'visual noise' to improve underwater vision and deep sea exploration Mar 31, 2005 #2 Integral Staff Emeritus Science Advisor Gold Member .1 mm on meter stick is gotten from a fair guess. You need to combine that fair guess with multiple measurements to obtain a statistical basis then compute an average. Your result should state a estimate at the magnitude different types of errors in measurement of your error, perhaps the standard deviation of your data. Integral, Mar 31, 2005 Mar 31, 2005 #3 whozum As far as significant figures go, if it is marked down to milimeters, the best measurement you can get is 0.0001m, you are allowed to guess one decimal place beyond what you can measure, provided you show a realm of error in the same magnitude. whozum, Mar 31, 2005 Apr 1, 2005 #4 brewnog Science Advisor Gold Member I've used metre sticks from which pretty precise readings could be taken, but the accuracy was really poor (perhaps 2mm out over the whole length). brewnog, Apr 1, 2005 Apr 1, 2005 #5 SpaceTiger Staff Emeritus Science Advisor Gold Member Haftred said: Can one read a meter stick down to a tenth of a millimeter? For example, could I reasonably measure an object as 32.43 cm using a meter stick? It's not clear to me that there's a rigorous justification for the standard error quote when using a meter stick, but it's also not clear that one is needed. If it's an accurate meter stick and you can resolve the markings with your eyes, then your measurement is certainly g
just how much the measured value is likely to deviate from the unknown, true, value of the quantity.
Uncertainty Of A Meter Stick
The art of estimating these deviations should probably be called uncertainty analysis, error calculation physics but for historical reasons is referred to as error analysis. This document contains brief discussions about how errors
How To Reduce Systematic Error
are reported, the kinds of errors that can occur, how to estimate random errors, and how to carry error estimates into calculated results. We are not, and will not be, https://www.physicsforums.com/threads/meter-stick.69423/ concerned with the “percent error” exercises common in high school, where the student is content with calculating the deviation from some allegedly authoritative number. Significant figures Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, http://www.owlnet.rice.edu/~labgroup/pdf/Error_analysis.htm you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m. Students frequently are confused about when to count a zero as a significant figure. The rule is: If the zero has a non-zero digit anywhere to its left, then the zero
avoided by performing a very careful measurement. Errors, on the other hand--cannot be avoided--even by the most careful observer. It is a common practice amongst the scientist to divide the errors into two broad categories: systematic http://www.utm.edu/~cerkal/lect2.htm errors and random errors. Systematic error: This type of error is the result of an improperly calibrated apparatus or and improperly designed experiment that introduces the same one directional bias into all of the measurements. A systematic error is an effect that changes all measurements by the same amount or by the same percentage. For example, a ruler that has a badly worn one end, will introduce the same amount of uncertainty (in this case systematic error systematic errors) is introduced to all measurements. Instrument zeroes should automatically be checked every time an instrument is used. Random Error: A random error is a result of fluctuations in experimental conditions (such as repetitive measurements) that cause a measured value to occur above or below the correct value with equal probability. For example, when we read the meter stick with naked eye in successive measurements, we may be unable to judge the position of of a meter the markings on the meter stick accurately enough to obtain repeatedly the same result. This results in fluctuations in the measured values. Sometimes, the fluctuations are intrinsic to the system under investigation (as in the radioactive source, where the number of the emerging radioactive particles arises from the basic nature of radioactive decay). These uncertainties (or errors) can be estimated by using statistical methods (average, standard deviation, mean, mode,). Note that there are other uncertainties, such as instrument uncertainty, which can be estimated by personal judgment. For example, the instrument uncertainty of a meter stick is usually 0.1 cm. Instrument Uncertainty: When an instrument is used in the laboratory, we should evaluate the uncertainty it introduces into the data collected. It is ideal to assume that each instrument is calibrated against a known standard. If this is the case the systematic errors are minimized. If, on the other hand, this procedure is not possible, we can estimate the systematic errors by comparing the measurements of the same physical quantity taken with different instruments in the laboratory. For instance, we can compare the measurements by using several meter sticks. If they all agree within one millimeter (this also happens to be the smallest division), we can view this one-millimeter as the uncertainty with which our meter stick would agree when compared (or calibrated) to a standard met