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QuestionA scientist measures 218kg218 \mathrm{kg}; the true value is 200kg200 \mathrm{kg}. Find absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is 218 kg218\,kg . The true value is 200 kg200\,kg

STEP 2

First, we need to calculate 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|

STEP 3

Now, plug in the given values for the measured value and true value to calculate the absolute error.
Absolute error=∣218 kg−200 kg∣Absolute\, error = |218\,kg -200\,kg|

STEP 4

Calculate the absolute error.
Absolute error=∣218 kg−200 kg∣=18 kgAbsolute\, error = |218\,kg -200\,kg| =18\,kg

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

Now, plug in the values for the absolute error and the true value to calculate the relative error.
Relative error=18 kg200 kgRelative\, error = \frac{18\,kg}{200\,kg}

STEP 7

Calculate the relative error. The result is a decimal value, which can be converted to a percentage by multiplying by100.
Relative error=18 kg200 kg=0.09Relative\, error = \frac{18\,kg}{200\,kg} =0.09Relative error=0.09×100=9%Relative\, error =0.09 \times100 =9\%The absolute error is 18 kg18\,kg and the relative error is 9%9\%.

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