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QuestionFind the absolute and relative error for a measurement of 146cm3146 \mathrm{cm}^3 when the true value is 100cm3100 \mathrm{cm}^3.

Studdy Solution

STEP 1

Assumptions1. The measured value is 146 cm3146 \, cm^3 . The true value is 100 cm3100 \, cm^3

STEP 2

First, we need to calculate 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|

STEP 3

Now, plug in the given values for the measured value and the true value to calculate the absolute error.
Absolute Error=∣146 cm3−100 cm3∣Absolute \, Error = |146 \, cm^3 -100 \, cm^3|

STEP 4

Calculate the absolute error.
Absolute Error=∣146 cm3−100 cm3∣=46 cm3Absolute \, Error = |146 \, cm^3 -100 \, cm^3| =46 \, cm^3

STEP 5

Next, we need to calculate 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}

STEP 6

Plug in the values for the absolute error and the true value to calculate the relative error.
Relative Error=46 cm3100 cm3Relative \, Error = \frac{46 \, cm^3}{100 \, cm^3}

STEP 7

Calculate the relative error and convert it to a percentage.
Relative Error=46 cm3100 cm3=0.46=46%Relative \, Error = \frac{46 \, cm^3}{100 \, cm^3} =0.46 =46\%The absolute error of the scientist's measurement is 46 cm346 \, cm^3 and the relative error is 46%46\%.

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