Question

If true value of a number is 36.25 and its absolute error is 0.002. Find the relative error and percentage error.

Answer 1

Answer:

percent error =$5.51\times10^-^3$ , relative error = $5.51\times10^-^5$

Step-by-step explanation:

Since, we know that:

Relative error = $\frac{absolute error}{true value}$

Absolute error is the difference between the measured value of a quantity and its actual value.

Absolute error =$\left | x-x' \right |$

where; x = true value, x'= approximate value

Absolute error = $\left | 36.25-x' \right |$

$\pm0.002 = 36.25-x'$

x'=36.248, 36.252

These are approximate values.

relative error = $\frac{o.oo2}{36.25}$

relative error = $5.51\times10^-^5$

percentage error = $\left |\frac{x-x'}{ x} \right |\times 100$

so, percent error = $\frac{o.oo2}{36.25}\times100$

percent error =$5.51\times10^-^3$