Error In Measurement Using Ruler
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a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this what is relative error site About Us Learn more about Stack Overflow the company Business Learn absolute error formula more about hiring developers or posting ads with us Physics Questions Tags Users Badges Unanswered Ask Question _ Physics what is absolute error Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute: Sign up Here's how it works: Anybody can errors in measurement physics ask a question Anybody can answer The best answers are voted up and rise to the top What is the error in a ruler? up vote 2 down vote favorite 2 I'm having trouble understanding simple error analysis of a ruler. Suppose we have this ruler. There is a mark for every centimeter. The precision is half a centimeter. This should mean
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that the rulermaker guarantees us that about 68% of the time (I don't think this is true in most cases), the true value will be in the interval $(x-0.5 \mathrm{cm}, x+0.5 \mathrm{cm})$. This is because de ruler/marks don't have the exact lenght. If the ruler reads $2\mathrm{cm}$, when it should be $2.5\mathrm{cm}$, what would the error at the $1\mathrm{cm}$ be? If the ruler is a bit too long wouldn't this be reflected for every mark? Is this the correct interpretation of uncertainty? Why isn't there less error when the tip of the object we want to measure coincides with a mark of the ruler? And if we don't measure the object from the tip of the ruler($0\mathrm{cm}$), so we have to calculate the difference, should we have to double the error? experimental-physics error-analysis share|cite|improve this question asked Dec 9 '14 at 23:34 jinawee 6,92132362 I think you're confusing accuracy and precision. The ruler is only precise to within a half cm (to the eye of the user) while it's only as accurate as the spacing was made correctly. Using your picture, I ca
of Accuracy Accuracy depends on the instrument you are measuring with. But as a general rule: The degree of accuracy is half a unit each side of the unit of measure Examples: When your instrument measures in "1"s then any value between 6½ and 7½ is measured as "7" When your
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instrument measures in "2"s then any value between 7 and 9 is measured as "8" Plus or absolute error example Minus We can show the error using the "Plus or Minus" sign: ± When the value could be between 6½ and 7½ 7 ±0.5 The error relative error formula is ±0.5 When the value could be between 7 and 9 8 ±1 The error is ±1 Example: a fence is measured as 12.5 meters long, accurate to 0.1 of a meter Accurate to 0.1 m means it could be up to http://physics.stackexchange.com/questions/151473/what-is-the-error-in-a-ruler 0.05 m either way: Length = 12.5 ±0.05 m So it could really be anywhere between 12.45 m and 12.55 m long. Absolute, Relative and Percentage Error The Absolute Error is the difference between the actual and measured value But ... when measuring we don't know the actual value! So we use the maximum possible error. In the example above the Absolute Error is 0.05 m What happened to the ± ... ? Well, we just want the size (the absolute value) of the difference. The Relative http://www.mathsisfun.com/measure/error-measurement.html Error is the Absolute Error divided by the actual measurement. We don't know the actual measurement, so the best we can do is use the measured value: Relative Error = Absolute Error Measured Value The Percentage Error is the Relative Error shown as a percentage (see Percentage Error). Let us see them in an example: Example: fence (continued) Length = 12.5 ±0.05 m So: Absolute Error = 0.05 m And: Relative Error = 0.05 m = 0.004 12.5 m And: Percentage Error = 0.4% More examples: Example: The thermometer measures to the nearest 2 degrees. The temperature was measured as 38° C The temperature could be up to 1° either side of 38° (i.e. between 37° and 39°) Temperature = 38 ±1° So: Absolute Error = 1° And: Relative Error = 1° = 0.0263... 38° And: Percentage Error = 2.63...% Example: You measure the plant to be 80 cm high (to the nearest cm) This means you could be up to 0.5 cm wrong (the plant could be between 79.5 and 80.5 cm high) Height = 80 ±0.5 cm So: Absolute Error = 0.5 cm And: Relative Error = 0.5 cm = 0.00625 80 cm And: Percentage Error = 0.625% Area When working out areas you need to think about both the width and length ... they could both be the smallest possible measure, or both the largest. Example: Alex measured the field to the nearest meter, and got a width of 6 m and a length of 8 m. Me
"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 https://www2.southeastern.edu/Academics/Faculty/rallain/plab194/error.html way to show the range of values is: measurement = best estimate ± uncertainty Example: a measurement of 5.07 g ± 0.02 g means that the experimenter is confident that the actual value for the quantity being measured lies between 5.05 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 absolute error estimating this uncertainty is what error analysis is all about). How 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 errors in measurement Correct: 52 cm ± 4 cm Always round the experimental measurement or result to the same 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 suff