Percentage Error Of Ruler
Contents |
a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this 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
Relative Error
Ask Question _ Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; relative error formula it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What is the error in a ruler? absolute error calculator 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 be in the interval $(x-0.5 \mathrm{cm}, x+0.5 \mathrm{cm})$. This is because de ruler/marks
Relative Error Calculator
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. Not that this is a full answer, but maybe that will help refine the question/answers. –tpg2114 Dec 9 '14 at 23:40 This is really a terrific question, and one that deserves a good answer that includes issues of discretiza
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 types of errors in measurement measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is absolute error example measured as "8" Plus or Minus We can show the error using the "Plus or Minus" sign: ± When the value could be between
Percentage Error Definition
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, accurate to 0.1 of a meter Accurate to http://physics.stackexchange.com/questions/151473/what-is-the-error-in-a-ruler 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 is 0.05 m What happened to the ± ... ? Well, https://www.mathsisfun.com/measure/error-measurement.html 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 When working out areas you need to think about both the width and length ... they could both be the smallest possible measure,
Example: I estimated 260 people, but 325 came. 260 − 325 = −65, ignore the "−" sign, so my error is 65 "Percentage Error": show the error as a percent https://www.mathsisfun.com/numbers/percentage-error.html of the exact value ... so divide by the exact value and make http://www.studyphysics.ca/newnotes/20/unit01_kinematicsdynamics/chp02_intro/lesson05.htm it a percentage: 65/325 = 0.2 = 20% Percentage Error is all about comparing a guess or estimate to an exact value. See percentage change, difference and error for other options. How to Calculate Here is the way to calculate a percentage error: Step 1: Calculate the error (subtract one value form the absolute error other) ignore any minus sign. Step 2: Divide the error by the exact value (we get a decimal number) Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign) As A Formula This is the formula for "Percentage Error": |Approximate Value − Exact Value| × 100% |Exact Value| (The "|" symbols mean absolute value, so negatives become percentage error of positive) Example: I thought 70 people would turn up to the concert, but in fact 80 did! |70 − 80| |80| × 100% = 10 80 × 100% = 12.5% I was in error by 12.5% Example: The report said the carpark held 240 cars, but we counted only 200 parking spaces. |240 − 200| |200| × 100% = 40 200 × 100% = 20% The report had a 20% error. We can also use a theoretical value (when it is well known) instead of an exact value. Example: Sam does an experiment to find how long it takes an apple to drop 2 meters. The theoreticalvalue (using physics formulas)is 0.64 seconds. But Sam measures 0.62 seconds, which is an approximate value. |0.62 − 0.64| |0.64| × 100% = 0.02 0.64 × 100% = 3% (to nearest 1%) So Sam was only 3% off. Without "Absolute Value" We can also use the formula without "Absolute Value". This can give a positive or negative result, which may be useful to know. Approximate Value − Exact Value × 100% Exact Value Example: They forecast 20 mm of rain, but we really got 25 m
Example 1: Your thermometer was dropped and has small air bubbles in it. improper or sloppy use of measuring device Example 2: When you used your thermometer, you measured the values in Fahrenheit instead of Celsius. ambient conditions (temperature, pressure, etc.) Example 3: Measuring the length of a piece of wood outdoors in the winter using a metal ruler, you forget that metal contracts in the cold making the ruler shorter. Whatever the scale (units) on a measuring device, the error you should record is one half of the smallest division. Often this is stated as the "possible error" in the measurement. Example 4: If you measure the length of a pencil using a regular ruler (they usually have 1 mm divisions) and find that it is 102 mm long, you should write down… 102 ± 0.5 mm The "plus-or-minus" (±) means "give-or-take" this much as the possible error. The length of the pencil could be as little as 101.5 mm, or as much as 102.5 mm. At times, there may be an accepted value for a measurement (verified in laboratories with very high standards). Some of these numbers are on the back of your data sheet. They are usually given with three sig digs. It is often useful to compare your measurement to this accepted value in order to evaluate how accurate you were. Calculating Errors There are three common ways to calculate your error: absolute error, percentage difference, and percentage error. Absolute Error is when you subtract the accepted value from your measured value… Absolute Error = Measured Value - Accepted Value A positive answer means you are over the accepted value. A negative answer means you are under the accepted value Percentage Error is the most common way of measuring an error, and often the most easy to understand. Percentage Error = Absolute Error / Accepted Value So, if you measured a pencil to be 102mm long, and an independent lab with high tech equipment measured it as 104mm,