QuestionA scientist measures $536 \, \mathrm{g} \, \mathrm{m}^{-3}$ ; true value is $1000 \, \mathrm{g} \, \mathrm{m}^{-3}$ . Find absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is $536 \, \mathrm{g} \, \mathrm{m}^{-3}$ . The true value is $1000 \, \mathrm{g} \, \mathrm{m}^{-3}$

STEP 2

First, we need to find the absolute error. The absolute error is the 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.
$Absolute\, Error = |536 \, \mathrm{g} \, \mathrm{m}^{-3} -1000 \, \mathrm{g} \, \mathrm{m}^{-3}|$

STEP 4

Calculate the absolute error.
$Absolute\, Error = |-464 \, \mathrm{g} \, \mathrm{m}^{-3}| =464 \, \mathrm{g} \, \mathrm{m}^{-3}$

STEP 5

Next, we need to find 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 given values for the absolute error and the true value to calculate the relative error.
$Relative\, Error = \frac{464 \, \mathrm{g} \, \mathrm{m}^{-3}}{1000 \, \mathrm{g} \, \mathrm{m}^{-3}}$

STEP 7

Calculate the relative error.
$Relative\, Error =0.464$ The relative error is usually expressed as a percentage.
$Relative\, Error =0.464 \times100\% =46.4\%$ The absolute error of the scientist's measurement is $464 \, \mathrm{g} \, \mathrm{m}^{-3}$ and the relative error is $46.4\%$ .

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QuestionA scientist measures $536 \, \mathrm{g} \, \mathrm{m}^{-3}$ ; true value is $1000 \, \mathrm{g} \, \mathrm{m}^{-3}$ . Find absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is $536 \, \mathrm{g} \, \mathrm{m}^{-3}$ . The true value is $1000 \, \mathrm{g} \, \mathrm{m}^{-3}$

STEP 2

First, we need to find the absolute error. The absolute error is the 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.
$Absolute\, Error = |536 \, \mathrm{g} \, \mathrm{m}^{-3} -1000 \, \mathrm{g} \, \mathrm{m}^{-3}|$

STEP 4

Calculate the absolute error.
$Absolute\, Error = |-464 \, \mathrm{g} \, \mathrm{m}^{-3}| =464 \, \mathrm{g} \, \mathrm{m}^{-3}$

STEP 5

Next, we need to find 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 given values for the absolute error and the true value to calculate the relative error.
$Relative\, Error = \frac{464 \, \mathrm{g} \, \mathrm{m}^{-3}}{1000 \, \mathrm{g} \, \mathrm{m}^{-3}}$

STEP 7

Calculate the relative error.
$Relative\, Error =0.464$ The relative error is usually expressed as a percentage.
$Relative\, Error =0.464 \times100\% =46.4\%$ The absolute error of the scientist's measurement is $464 \, \mathrm{g} \, \mathrm{m}^{-3}$ and the relative error is $46.4\%$ .

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QuestionA scientist measures 536 g m−3536 \, \mathrm{g} \, \mathrm{m}^{-3}536gm−3; true value is 1000 g m−31000 \, \mathrm{g} \, \mathrm{m}^{-3}1000gm−3. Find absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is 536 g m−3536 \, \mathrm{g} \, \mathrm{m}^{-3}536gm−3 . The true value is 1000 g m−31000 \, \mathrm{g} \, \mathrm{m}^{-3}1000gm−3

STEP 2

First, we need to find the absolute error. The absolute error is the difference between the measured value and the true value.Absolute Error=∣Measured Value−True Value∣Absolute\, Error = |Measured\, Value - True\, Value|AbsoluteError=∣MeasuredValue−TrueValue∣

STEP 3

Now, plug in the given values for the measured value and the true value to calculate the absolute error.Absolute Error=∣536 g m−3−1000 g m−3∣Absolute\, Error = |536 \, \mathrm{g} \, \mathrm{m}^{-3} -1000 \, \mathrm{g} \, \mathrm{m}^{-3}|AbsoluteError=∣536gm−3−1000gm−3∣

STEP 4

Calculate the absolute error.Absolute Error=∣−464 g m−3∣=464 g m−3Absolute\, Error = |-464 \, \mathrm{g} \, \mathrm{m}^{-3}| =464 \, \mathrm{g} \, \mathrm{m}^{-3}AbsoluteError=∣−464gm−3∣=464gm−3

STEP 5

Next, we need to find the relative error. The relative error is the absolute error divided by the true value.Relative Error=Absolute ErrorTrue ValueRelative\, Error = \frac{Absolute\, Error}{True\, Value}RelativeError=TrueValueAbsoluteError​

STEP 6

Now, plug in the given values for the absolute error and the true value to calculate the relative error.Relative Error=464 g m−31000 g m−3Relative\, Error = \frac{464 \, \mathrm{g} \, \mathrm{m}^{-3}}{1000 \, \mathrm{g} \, \mathrm{m}^{-3}}RelativeError=1000gm−3464gm−3​

STEP 7

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QuestionA scientist measures $536 \, \mathrm{g} \, \mathrm{m}^{-3}$ ; true value is $1000 \, \mathrm{g} \, \mathrm{m}^{-3}$ . Find absolute and relative error.

Assumptions1. The measured value is $536 \, \mathrm{g} \, \mathrm{m}^{-3}$ . The true value is $1000 \, \mathrm{g} \, \mathrm{m}^{-3}$

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

Now, plug in the given values for the measured value and the true value to calculate the absolute error.
$Absolute\, Error = |536 \, \mathrm{g} \, \mathrm{m}^{-3} -1000 \, \mathrm{g} \, \mathrm{m}^{-3}|$

Calculate the absolute error.
$Absolute\, Error = |-464 \, \mathrm{g} \, \mathrm{m}^{-3}| =464 \, \mathrm{g} \, \mathrm{m}^{-3}$

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

Now, plug in the given values for the absolute error and the true value to calculate the relative error.
$Relative\, Error = \frac{464 \, \mathrm{g} \, \mathrm{m}^{-3}}{1000 \, \mathrm{g} \, \mathrm{m}^{-3}}$