Error In A Ruler
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Percentage Error Of A Metre Ruler
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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 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 what is absolute error 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 can make that measurement 5 times and say that it's between, say, 10.3 and 10.5 each time. That's precision. But it really could be 15 because the hash marks are wrong, that's accuracy. Not that this is a full answer, but maybe that will help refine the question/answers. &
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 Minus
Type Of Error In Measurement
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 is relative error formula ±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 0.05 m http://physics.stackexchange.com/questions/151473/what-is-the-error-in-a-ruler 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 Error is http://www.mathsisfun.com/measure/error-measurement.html 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. Measuring to the nearest met
instrument used. In the photo below, the red rectangle measures someplace between 2.3 and 2.4 cm long. We must estimate its length, http://science.halleyhosting.com/sci/ibbio/inquiry/error/precision.htm and that thus imparts a source of error in our measurement. We can determine the degree of precision of any scientific device we are using (metric ruler, balance beam, pipette, graduated cylinder, etc.) by finding the smallest division on the instrument. In the photo above, the degree of precision is 1 mm (or 0.1 cm) since that is the error in smallest division we can see without estimating. The measurement of the red rectangle above would thus be measured at 2.35 cm +/- 0.1 cm. The +/- 0.1 cm in this case lets us know how precise the metric ruler is, and this should be recorded at the top any column in a data table where a measurement has error in a been taken using this device! We need to consider the degree of precision of the measuring devise when making measurements. If you are measuring small quantities, then you need to use equipment that is more precise to avoid a greater potential for error! If we measure the blue rectangle above, we will note that it is about 0.33 cm +/- 0.1 cm long. Note that the error of 0.1 cm is a large percentage ( about 30%) of the measurement! This is not very precise! We would thus need to use a ruler that measures to smaller divisions (like 10ths of a mm or perhaps 1/2 mm) to lower this margin of error to more respectable levels. Displaying Precision Measurements in Data Tables Note that the precision of the metric ruler that was used is indicated next to the appropriate label in parentheses at the top of the table. This, like the units, is listed only once so you don't have to constantly repeat it behind each number in the table! [Review] Slichter
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