Error In Ruler
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The difference between two measurements is called a variation in the measurements. Another word for this variation - or uncertainty in measurement - is "error." This "error" is not the same as a "mistake." It does not mean that you got the wrong answer. error in ruler measurement The error in measurement is a mathematical way to show the uncertainty in the measurement. It uncertainty of a ruler in inches is the difference between the result of the measurement and the true value of what you were measuring. The precision of a measuring instrument is determined uncertainty of a ruler in mm by the smallest unit to which it can measure. The precision is said to be the same as the smallest fractional or decimal division on the scale of the measuring instrument. Ways of Expressing Error in Measurement: 1. Greatest Possible how to calculate absolute error Error: Because no measurement is exact, measurements are always made to the "nearest something", whether it is stated or not. The greatest possible error when measuring is considered to be one half of that measuring unit. For example, you measure a length to be 3.4 cm. Since the measurement was made to the nearest tenth, the greatest possible error will be half of one tenth, or 0.05. 2. Tolerance intervals: Error in measurement may be represented by a tolerance interval (margin of
Absolute Error Formula
error). Machines used in manufacturing often set tolerance intervals, or ranges in which product measurements will be tolerated or accepted before they are considered flawed. To determine the tolerance interval in a measurement, add and subtract one-half of the precision of the measuring instrument to the measurement. For example, if a measurement made with a metric ruler is 5.6 cm and the ruler has a precision of 0.1 cm, then the tolerance interval in this measurement is 5.6 0.05 cm, or from 5.55 cm to 5.65 cm. Any measurements within this range are "tolerated" or perceived as correct. Accuracy is a measure of how close the result of the measurement comes to the "true", "actual", or "accepted" value. (How close is your answer to the accepted value?) Tolerance is the greatest range of variation that can be allowed. (How much error in the answer is occurring or is acceptable?) 3. Absolute Error and Relative Error: Error in measurement may be represented by the actual amount of error, or by a ratio comparing the error to the size of the measurement. The absolute error of the measurement shows how large the error actually is, while the relative error of the measurement shows how large the error is in relation to the correct value. Absolute errors do not always give an indication of how important the error may be. If you are measuring a football field and the absolute error is 1 cm, the error is virtually irrelevant. But, if
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
What Is Absolute Error
unit of measure Examples: When your instrument measures in "1"s then any value relative error formula between 6½ and 7½ is measured as "7" When your instrument measures in "2"s then any value between 7 and absolute error calculator 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 http://www.regentsprep.org/regents/math/algebra/am3/LError.htm The error 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 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 http://www.mathsisfun.com/measure/error-measurement.html 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 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 &plus
Community Forums > Physics > General Physics > 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 rule? Page https://www.physicsforums.com/threads/what-is-the-uncertainty-in-a-metre-rule.610200/ 1 of 3 1 2 3 Next > May 30, 2012 #1 mutineer123 WHat is the 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 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 - absolute error latest science and technology news stories on Phys.org •Metamaterial uses light to control its motion •Stable molecular state of photons and artificial atom discovered •Self-learning computer tackles problems beyond the reach of previous systems 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 error in ruler 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 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