QuestionCalculate the absolute and relative error for a measurement of $581 \mathrm{g} \cdot \mathrm{m}^{-3}$ vs. true value $500 \mathrm{g} \cdot \mathrm{m}^{-3}$ .

Studdy Solution

STEP 1

Assumptions1. The measured value is $581 \, \mathrm{g} \cdot \mathrm{m}^{-3}$ . The true value is $500 \, \mathrm{g} \cdot \mathrm{m}^{-3}$

STEP 2

First, we need to find the absolute error. The absolute error is the absolute difference between the true value and the measured 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.
$Absolute\, Error = |581 \, \mathrm{g} \cdot \mathrm{m}^{-3} -500 \, \mathrm{g} \cdot \mathrm{m}^{-3}|$

STEP 4

Calculate the absolute error.
$Absolute\, Error = |581 \, \mathrm{g} \cdot \mathrm{m}^{-3} -500 \, \mathrm{g} \cdot \mathrm{m}^{-3}| =81 \, \mathrm{g} \cdot \mathrm{m}^{-3}$

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.
$Relative\, Error = \frac{81 \, \mathrm{g} \cdot \mathrm{m}^{-3}}{500 \, \mathrm{g} \cdot \mathrm{m}^{-3}}$

STEP 7

Calculate the relative error.
$Relative\, Error = \frac{81 \, \mathrm{g} \cdot \mathrm{m}^{-3}}{500 \, \mathrm{g} \cdot \mathrm{m}^{-3}} =0.162$ The absolute error is $81 \, \mathrm{g} \cdot \mathrm{m}^{-3}$ and the relative error is $0.162$ or $16.2\%$ .

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QuestionCalculate the absolute and relative error for a measurement of $581 \mathrm{g} \cdot \mathrm{m}^{-3}$ vs. true value $500 \mathrm{g} \cdot \mathrm{m}^{-3}$ .

Studdy Solution

STEP 1

Assumptions1. The measured value is $581 \, \mathrm{g} \cdot \mathrm{m}^{-3}$ . The true value is $500 \, \mathrm{g} \cdot \mathrm{m}^{-3}$

STEP 2

First, we need to find the absolute error. The absolute error is the absolute difference between the true value and the measured 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.
$Absolute\, Error = |581 \, \mathrm{g} \cdot \mathrm{m}^{-3} -500 \, \mathrm{g} \cdot \mathrm{m}^{-3}|$

STEP 4

Calculate the absolute error.
$Absolute\, Error = |581 \, \mathrm{g} \cdot \mathrm{m}^{-3} -500 \, \mathrm{g} \cdot \mathrm{m}^{-3}| =81 \, \mathrm{g} \cdot \mathrm{m}^{-3}$

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.
$Relative\, Error = \frac{81 \, \mathrm{g} \cdot \mathrm{m}^{-3}}{500 \, \mathrm{g} \cdot \mathrm{m}^{-3}}$

STEP 7

Calculate the relative error.
$Relative\, Error = \frac{81 \, \mathrm{g} \cdot \mathrm{m}^{-3}}{500 \, \mathrm{g} \cdot \mathrm{m}^{-3}} =0.162$ The absolute error is $81 \, \mathrm{g} \cdot \mathrm{m}^{-3}$ and the relative error is $0.162$ or $16.2\%$ .

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QuestionCalculate the absolute and relative error for a measurement of 581g⋅m−3581 \mathrm{g} \cdot \mathrm{m}^{-3}581g⋅m−3 vs. true value 500g⋅m−3500 \mathrm{g} \cdot \mathrm{m}^{-3}500g⋅m−3.

Studdy Solution

STEP 1

Assumptions1. The measured value is 581 g⋅m−3581 \, \mathrm{g} \cdot \mathrm{m}^{-3}581g⋅m−3 . The true value is 500 g⋅m−3500 \, \mathrm{g} \cdot \mathrm{m}^{-3}500g⋅m−3

STEP 2

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

STEP 3

STEP 4

Calculate the absolute error.Absolute Error=∣581 g⋅m−3−500 g⋅m−3∣=81 g⋅m−3Absolute\, Error = |581 \, \mathrm{g} \cdot \mathrm{m}^{-3} -500 \, \mathrm{g} \cdot \mathrm{m}^{-3}| =81 \, \mathrm{g} \cdot \mathrm{m}^{-3}AbsoluteError=∣581g⋅m−3−500g⋅m−3∣=81g⋅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=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=81 g⋅m−3500 g⋅m−3Relative\, Error = \frac{81 \, \mathrm{g} \cdot \mathrm{m}^{-3}}{500 \, \mathrm{g} \cdot \mathrm{m}^{-3}}RelativeError=500g⋅m−381g⋅m−3​

STEP 7

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QuestionCalculate the absolute and relative error for a measurement of $581 \mathrm{g} \cdot \mathrm{m}^{-3}$ vs. true value $500 \mathrm{g} \cdot \mathrm{m}^{-3}$ .

Assumptions1. The measured value is $581 \, \mathrm{g} \cdot \mathrm{m}^{-3}$ . The true value is $500 \, \mathrm{g} \cdot \mathrm{m}^{-3}$

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

Calculate the absolute error.
$Absolute\, Error = |581 \, \mathrm{g} \cdot \mathrm{m}^{-3} -500 \, \mathrm{g} \cdot \mathrm{m}^{-3}| =81 \, \mathrm{g} \cdot \mathrm{m}^{-3}$

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.
$Relative\, Error = \frac{81 \, \mathrm{g} \cdot \mathrm{m}^{-3}}{500 \, \mathrm{g} \cdot \mathrm{m}^{-3}}$