Reading Ruler Error
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Absolute Error Formula
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Type Of Error In Measurement
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 that the rulermaker guarantees us that about 68% of the time (I don't think this is absolute error calculator 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 6,93132362 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
Community Forums > Physics > General Physics > We've just passed 300 Insights! View them here! What a resource! Dismiss Notice Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math community on the planet! Everyone who loves science is here! WHat is the uncertainty in a metre
Relative Error Calculator
rule? Page 1 of 3 1 2 3 Next > May 30, 2012 #1 mutineer123 WHat is the
Absolute Error Example
uncertainty in a metre rule?? For a single value is it 1 mm or is it 1/2mm(half the smallest division) ? And what about measuring something how to find absolute error like a length of a stick (we need to take 2 readings, and deduct them like 15-0=15), then is the uncertainty 1+1=2mm or is it .5+.5=1mm ? mutineer123, May 30, 2012 Phys.org - latest science and technology news stories on Phys.org •The quantum http://physics.stackexchange.com/questions/151473/what-is-the-error-in-a-ruler sniffer dog •Light-driven atomic rotations excite magnetic waves •Clearing 'visual noise' to improve underwater vision and deep sea exploration May 30, 2012 #2 K^2 Science Advisor Re: WHat is the uncertainty in a metre rule?? The rule is half the smallest division. So if your ruler has 1mm divisions, then the error is 0.5mm. [strike]I believe, the errors do add. So it does sound like 0.5mm+0.5mm = 1mm is the correct answer there, but I'm less certain about that.[/strike] Last edited: May 31, 2012 K^2, May https://www.physicsforums.com/threads/what-is-the-uncertainty-in-a-metre-rule.610200/ 30, 2012 May 31, 2012 #3 Studiot Re: WHat is the uncertainty in a metre rule?? So it does sound like 0.5mm+0.5mm = 1mm is the correct answer there, but I'm less certain about that. Do you not think it should be [tex]\sqrt {{{\left( {0.5} \right)}^2} + {{\left( {0.5} \right)}^2}} = 0.7mm[/tex] For a single value is it 1 mm or is it 1/2mm(half the smallest division) ? And what about measuring something like a length of a stick (we need to take 2 readings, and deduct them like 15-0=15), then is the uncertainty 1+1=2mm or is it .5+.5=1mm ? That rather depends upon your ruler. If it is a school type ruler which does not have zero at the end of the ruler then yes you have two measurements as above. If it is an engineer's rule with zero flush ground to one end then there is only one comparison to account for. Last edited: May 31, 2012 Studiot, May 31, 2012 May 31, 2012 #4 mfb Insights Author 2015 Award Staff: Mentor Re: WHat is the uncertainty in a metre rule?? I would not expect that the ruler has an accuracy of .5mm over the full range of a meter. While it is possible to read the values with an even higher accuracy, the scale itself might be wrong by 1-2 mm. mfb, May 31, 2012 May 31, 2012 #5 Studiot Re: WHat is the uncertainty in a metre rule?? I would not expect that the ruler has an accuracy of .5mm over the full range
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 https://www.mathsisfun.com/measure/error-measurement.html measure Examples: When your instrument measures in "1"s then any value between 6½ and 7½ is measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is measured as "8" Plus or 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 is absolute error ±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 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 reading ruler error 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 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
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