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QuestionA scientist measures 891kg891 \mathrm{kg}; true value is 700kg700 \mathrm{kg}. Find absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is 891 kg891\, kg . The true value is 700 kg700\, kg

STEP 2

First, we need to find the absolute error. The absolute error is the absolute value of the 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=∣891 kg−700 kg∣Absolute\, error = |891\, kg -700\, kg|

STEP 4

Calculate the absolute error.
Absolute error=∣891 kg−700 kg∣=191 kgAbsolute\, error = |891\, kg -700\, kg| =191\, kg

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}

STEP 6

Now, plug in the given values for the absolute error and true value to calculate the relative error.
Relative error=191 kg700 kgRelative\, error = \frac{191\, kg}{700\, kg}

STEP 7

Calculate the relative error.
Relative error=191 kg700 kg=0.273Relative\, error = \frac{191\, kg}{700\, kg} =0.273

STEP 8

The relative error is usually expressed as a percentage. To convert the decimal to a percentage, multiply by100.
Relative error=0.273×100%Relative\, error =0.273 \times100\%

STEP 9

Calculate the relative error percentage.
Relative error=.273×100%=27.3%Relative\, error =.273 \times100\% =27.3\%The absolute error is 191 kg191\, kg and the relative error is 27.3%27.3\%.

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