Greatest Possible Error Of Measurements
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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 greatest possible error calculator "error." This "error" is not the same as a "mistake." It does what is relative error not mean that you got the wrong answer. The error in measurement is a mathematical way to show the absolute error formula uncertainty in the measurement. It 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 by
Absolute Error Calculator
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 Error: Because no measurement is exact, measurements are always made to the "nearest something", whether it is stated or not. The greatest possible error what is absolute 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 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
number you enter is. Enter a number followed by the unit. However, leave a space between the number and the unit. This calculator will help you master the concept. relative error formula Greatest possible error What is the greatest possible
Absolute Error Example
error (GPE)? No measurement is perfect. Whenever you are doing some measurement, there is a great likelihood that it is not
Types Of Errors In Measurement
exact.Definition: The greatest possible error in a measurement is half of the measuring unit.For example, what is the greatest possible error for 8 cm?8 cm was measured to the nearest 1 cm, so the measuring http://www.regentsprep.org/regents/math/algebra/am3/LError.htm unit is 1 cm. The greatest possible error is 0.5 times 1 or 0.5 cm.What is the GPE for 4.2 inches?This time 4.2 was measured to the nearest tenth of an inch or 0.1 inch, so the measuring unit is 0.1. The GPE is 0.5 times 0.1 inch or 0.05 inch. Real life application of the greatest possible error You measure a garden that is rectangular as http://www.basic-mathematics.com/greatest-possible-error-calculator.html shown in the diagram. Find the minimum and maximum area of the garden. The measurements were made to the nearest foot, so the greatest possible error is 0.5 foot. The width of the garden could be as little as 27 - 0.5 = 26.5 or as big as 27 + 0.5 = 27.5The length of the garden could be as little as 18 - 0.5 = 17.5 or as big as 18 + 0.5 = 18.5 The minimum area = 26.5 × 17.5 = 463.75 square feet The maximum area = 27.5 &$215; 18.5 = 508.75 square feet New math lessons Email First Name (optional) Subscribe Your email is safe with us. We will only use it to inform you about new math lessons. IntroductionHomepageMath blogAbout meArithmeticBasic OperationsAncient numerationNumber theorySet notationWhole numbersRounding and estimatingFractionsDecimalsRatio and proportionPercentageBasic math word problemsConsumer mathNumber propertiesMetric systemBasic math puzzlesCool math tricksBasic math calculatorFun Online Math GamesGeometryBasic geometryPerimeterArea of shapesCommon geometry formulasWhat is a circle?Volume of solidsSurface area of solidsPythagorean theoremStraightedge and compass constructionCongruent ShapesTessellationsSlope/Standard formGeometry calculatorGeometry word problemsGeometry proofsAlgebra / TrigTypes of GraphsExponentRational numbersIntroduction to algebraGraphing/InequalitiesAbsolute valueSystem of linear equationsPolynomialsFactoring: hot topicsSolving quadratic equationsMatricesSequences and patternsAlgebra word problemsWhat is Trigonometry?Probability and StatisticsProbabilityStatisticsTeachers/StudentsFree math problem solverK-12 testsGED math testBasic math testAlgebra testBasic mathematics workshe
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 http://www.mathsisfun.com/measure/error-measurement.html 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 ±0.5 When the absolute error 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 and Percentage Error The Absolute greatest possible error 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 Error = 1° = 0.0263... 38° And: Percentage E