QuestionA scientist measures $561 \mathrm{g/m}^3$ ; the true value is $400 \mathrm{g/m}^3$ . Find absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is $561 g/m^3$ . The true value is $400 g/m^3$
3. Absolute error is calculated as the absolute difference between the measured value and the true value4. Relative error is calculated as the absolute error divided by the true value

STEP 2

First, we calculate the absolute error. This is done by subtracting the true value from the measured value and taking the absolute value of the result.
$Absolute\, error = |Measured\, value - True\, value|$

STEP 3

Now, plug in the given values for the measured value and true value to calculate the absolute error.
$Absolute\, error = |561 g/m^3 -400 g/m^3|$

STEP 4

Calculate the absolute error.
$Absolute\, error = |561 g/m^3 -400 g/m^3| =161 g/m^3$

STEP 5

Next, we calculate the relative error. This is done by dividing the absolute error by the true value.
$Relative\, error = \frac{Absolute\, error}{True\, value}$

STEP 6

Now, plug in the values for the absolute error and true value to calculate the relative error.
$Relative\, error = \frac{161 g/m^3}{400 g/m^3}$

STEP 7

Calculate the relative error.
$Relative\, error = \frac{161 g/m^3}{400 g/m^3} =0.4025$ The absolute error of the scientist's measurement is $161 g/m^3$ and the relative error is $0.4025$ or $40.25\%$ .

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