Maximum Percentage Error
Contents |
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 percentage error formula and 7½ is measured as "7" When your instrument measures in "2"s then any value
Percentage Error Chemistry
between 7 and 9 is measured as "8" Plus or Minus We can show the error using the "Plus or Minus" sign: ± percent error calculator When the value could be between 6½ and 7½ 7 ±0.5 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, can percent error be negative 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 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
Negative Percent 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 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 Whe
Community Forums > Science Education > Homework and Coursework Questions > Calculus and Beyond Homework > Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors Dismiss Notice Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math community on the planet! percent error worksheet Everyone who loves science is here! Estimating the maximum possible percentage error Aug 10, 2010 #1 benji123 what is a good percent error 1. The problem statement, all variables and given/known data Hi all! Im new to the forum, came across it from googling the problem which I had
Percent Error Definition
and someone was having difficuilty with a question like this on here! Here's the question I have... The coefficient of rigidity, n, of a wire of length L and uniform diameter d is given by n=AL/d^4 If A is a constant and https://www.mathsisfun.com/measure/error-measurement.html the parameters L and d are known to within ± 2% of their correct values, estimate the maximum possible percentage error in the calculated value of n. 2. Relevant equations n=AL/d^4 3. The attempt at a solution dn = dn/dL x dL + dn/dA x dA dn = A/d^4 dL + L/d^4 dA n = A/d^4 x ΔL + L/d^4 x ΔA n = ΔL/L + ΔA/A Where do I go from here? Any help will be greatly appreciated :) benji123, Aug 10, 2010 Phys.org https://www.physicsforums.com/threads/estimating-the-maximum-possible-percentage-error.421488/ - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Aug 10, 2010 #2 Mark44 Insights Author Staff: Mentor benji123 said: ↑ 1. The problem statement, all variables and given/known data Hi all! Im new to the forum, came across it from googling the problem which I had and someone was having difficuilty with a question like this on here! Here's the question I have... Welcome, benji. You have come to a good place for help. benji123 said: ↑ The coefficient of rigidity, n, of a wire of length L and uniform diameter d is given by n=AL/d^4 If A is a constant and the parameters L and d are known to within ± 2% of their correct values, estimate the maximum possible percentage error in the calculated value of n. 2. Relevant equations n=AL/d^4 3. The attempt at a solution dn = dn/dL x dL + dn/dA x dA A is a constant, so dn/dA doesn't make any sense. Instead, you want dn/dd. For the record, dn/dL and dn/dd are really the partial derivatives of n. I.e., [tex]\frac{\partial n}{\partial L} \text{and} \frac{\partial n}{\partial d}[/tex] benji123 said: ↑ dn = A/d^4 dL + L/d^4 dA n = A/d^4 x ΔL + L/d^4 x ΔA n = ΔL/L + ΔA/A Where do I go from here? Any help will be greatly appreciated :) For the percent change in n, you want d
5 inches, when the real length is 6 inches. Notice how the percentage of error increases as http://www.regentsprep.org/regents/math/algebra/am3/LErrorD.htm the student uses this measurement to compute surface area and volume. Measurement Compute Surface Area Compute Volume The side of a cube is measured. Measurement: 5 in. Actual size: 6 in. Percent of error = Surface area computed with measurement: SA = 25 • 6 = 150 sq. in. Actual surface area: percent error SA = 36 • 6 = 216 sq. in. Percent of error = Volume computed with measurement: V = 5 ³ = 125 cubic in.Actual volume: V = 6 ³ = 216 cubic in. Percent of error = rounded to nearest tenth. 2. A box has the measurements 1.4 maximum percentage error cm by 8.2 cm by 12.5 cm. Find the percent of error in calculating its volume. ANSWER: Since no other values are given, we will use the greatest possible error based upon the fact that these measurements were taken to the nearest tenth of a centimeter, which will be 0.05 cm. Volume as measured: 1.4 x 8.2 x 12.5 = 143.5 cubic cm Maximum volume (+0.05) : 1.45 x 8.25 x 12.55 = 150.129375 cubic cm Minimum volume (-0.05): 1.35 x 8.15 x 12.45 = 136.981125 cubic cm Possible error in volume: Maximum - measured = 6.629375 cubic cm Measured - minimum = 6.518875 cubic cm Use the "greatest" possible error in volume: 6.629375 cubic cm Remember that percent of error is the relative error times 100%. The percent of error is approximately 5%. Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts
be down. Please try the request again. Your cache administrator is webmaster. Generated Thu, 20 Oct 2016 13:01:12 GMT by s_wx1126 (squid/3.5.20)