Error Uncertainty Calculation
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dividing Is one result consistent with another? What if there are several measurements of the same quantity? How can one estimate the uncertainty of a slope on a graph? Uncertainty in a single uncertainty calculation formula measurement Bob weighs himself on his bathroom scale. The smallest divisions on
How To Calculate Uncertainty In Physics
the scale are 1-pound marks, so the least count of the instrument is 1 pound. Bob reads his how to calculate percentage uncertainty weight as closest to the 142-pound mark. He knows his weight must be larger than 141.5 pounds (or else it would be closer to the 141-pound mark), but smaller
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than 142.5 pounds (or else it would be closer to the 143-pound mark). So Bob's weight must be weight = 142 +/- 0.5 pounds In general, the uncertainty in a single measurement from a single instrument is half the least count of the instrument. Fractional and percentage uncertainty What is the fractional uncertainty in Bob's weight? uncertainty in weight fractional how to calculate uncertainty in excel uncertainty = ------------------------ value for weight 0.5 pounds = ------------- = 0.0035 142 pounds What is the uncertainty in Bob's weight, expressed as a percentage of his weight? uncertainty in weight percentage uncertainty = ----------------------- * 100% value for weight 0.5 pounds = ------------ * 100% = 0.35% 142 pounds Combining uncertainties in several quantities: adding or subtracting When one adds or subtracts several measurements together, one simply adds together the uncertainties to find the uncertainty in the sum. Dick and Jane are acrobats. Dick is 186 +/- 2 cm tall, and Jane is 147 +/- 3 cm tall. If Jane stands on top of Dick's head, how far is her head above the ground? combined height = 186 cm + 147 cm = 333 cm uncertainty in combined height = 2 cm + 3 cm = 5 cm combined height = 333 cm +/- 5 cm Now, if all the quantities have roughly the same magnitude and uncertainty -- as in the example above -- the result makes perfect sense. But if one tries to add together
"true value" exists based on how they define what is being measured (or calculated). Scientists reporting their results usually specify a range of values that they expect this "true value" to fall within. The most common way to show the range
Percentage Uncertainty Physics
of values is: measurement = best estimate ± uncertainty Example: a measurement of 5.07
Combining Uncertainties
g ± 0.02 g means that the experimenter is confident that the actual value for the quantity being measured lies between 5.05 percentage uncertainty definition g and 5.09 g. The uncertainty is the experimenter's best estimate of how far an experimental quantity might be from the "true value." (The art of estimating this uncertainty is what error analysis is all about). How http://spiff.rit.edu/classes/phys273/uncert/uncert.html many digits should be kept? Experimental uncertainties should be rounded to one significant figure. Experimental uncertainties are, by nature, inexact. Uncertainties are almost always quoted to one significant digit (example: ±0.05 s). If the uncertainty starts with a one, some scientists quote the uncertainty to two significant digits (example: ±0.0012 kg). Wrong: 52.3 cm ± 4.1 cm Correct: 52 cm ± 4 cm Always round the experimental measurement or result to the same https://www2.southeastern.edu/Academics/Faculty/rallain/plab194/error.html decimal place as the uncertainty. It would be confusing (and perhaps dishonest) to suggest that you knew the digit in the hundredths (or thousandths) place when you admit that you unsure of the tenths place. Wrong: 1.237 s ± 0.1 s Correct: 1.2 s ± 0.1 s Comparing experimentally determined numbers Uncertainty estimates are crucial for comparing experimental numbers. Are the measurements 0.86 s and 0.98 s the same or different? The answer depends on how exact these two numbers are. If the uncertainty too large, it is impossible to say whether the difference between the two numbers is real or just due to sloppy measurements. That's why estimating uncertainty is so important! Measurements don't agree 0.86 s ± 0.02 s and 0.98 s ± 0.02 s Measurements agree 0.86 s ± 0.08 s and 0.98 s ± 0.08 s If the ranges of two measured values don't overlap, the measurements are discrepant (the two numbers don't agree). If the rangesoverlap, the measurements are said to be consistent. Estimating uncertainty from a single measurement In many circumstances, a single measurement of a quantity is often sufficient for the purposes of the measurement being taken. But if you only take one measurement, how can you estimate the uncertainty in that measurement? Estimating the uncertainty in a single measurement
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