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Absolute, relative and percentage error

Measurement and errors · Physics

Study notes

Let us solve an example step by step. Suppose the true length of your study table is 200 centimeters. When you measure it with your plastic ruler, you find the length to be 196 centimeters. Let us find the absolute error, relative error, and percentage error. Step 1: Identify the true value and the measured value. True value = 200 cm, Measured value = 196 cm. Step 2: Calculate the Absolute Error. Absolute Error is the difference between the true value and the measured value. Formula: Absolute Error = | True Value - Measured Value |. Calculation: | 200 - 196 | = 4 cm. So, the absolute error is 4 centimeters. Step 3: Calculate the Relative Error. Relative Error compares the absolute error to the true value. Formula: Relative Error = Absolute Error / True Value. Calculation: 4 / 200 = 0.02. So, the relative error is 0.02. Step 4: Calculate the Percentage Error. Percentage Error turns the relative error into a percentage. Formula: Percentage Error = (Relative Error) * 100%. Calculation: 0.02 * 100 = 2%. So, the final percentage error is 2 percent.

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