QuestionA scientist measures $71.1 \mathrm{~m}$ ; the true value is $50.0 \mathrm{~m}$ . Find absolute and relative errors.

Studdy Solution

STEP 1

Assumptions1. The measured value is $71.1 \mathrm{~m}$ . The true value is $50.0 \mathrm{~m}$

STEP 2

First, we need to calculate the absolute error. The absolute error is the absolute difference between the measured value and the true value.
$Absolute\, Error = |Measured\, Value - True\, Value|$

STEP 3

Now, plug in the given values for the measured value and the true value to calculate the absolute error.
$Absolute\, Error = |71.1 \mathrm{~m} -50.0 \mathrm{~m}|$

STEP 4

Calculate the absolute error.
$Absolute\, Error = |71.1 \mathrm{~m} -50.0 \mathrm{~m}| =21.1 \mathrm{~m}$

STEP 5

Next, we need to calculate the relative error. The relative error is the absolute error divided by the true value.
$Relative\, Error = \frac{Absolute\, Error}{True\, Value}$

STEP 6

Now, plug in the values for the absolute error and the true value to calculate the relative error.
$Relative\, Error = \frac{21.1 \mathrm{~m}}{50.0 \mathrm{~m}}$

STEP 7

Calculate the relative error. $Relative\, Error = \frac{21.1 \mathrm{~m}}{50.0 \mathrm{~m}} =0.422$

STEP 8

The relative error is often expressed as a percentage. To convert the decimal to a percentage, multiply by100.
$Relative\, Error =0.422 \times100\%$

STEP 9

Calculate the relative error percentage.
$Relative\, Error =.422 \times100\% =42.2\%$ The absolute error is $21. \mathrm{~m}$ and the relative error is $42.2\%$ .

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