Question

find the absolute and relative errors in the following situation. your true height is 64.0 inches (54\), but a nurse in your doctors office measures your height as 63.8 inches. the absolute error is inches. (simplify your answer. round to the nearest tenth as needed.)

Explanation:

Step1: Recall absolute - error formula

The formula for absolute error is $| \text{True value}-\text{Measured value}|$.
Let the true value $T = 64.0$ inches and the measured value $M=63.8$ inches.
$|T - M|=|64.0 - 63.8|$

Step2: Calculate the absolute error

$|64.0 - 63.8|=0.2$ inches

Step3: Recall relative - error formula

The formula for relative error is $\frac{| \text{True value}-\text{Measured value}|}{\text{True value}}$.
Relative error $=\frac{|64.0 - 63.8|}{64.0}$

Step4: Calculate the relative error

$\frac{|64.0 - 63.8|}{64.0}=\frac{0.2}{64.0}= 0.003125$

Answer:

The absolute error is $0.2$ inches.
The relative error is $0.003125$.