Question

If true value is equal to 10/3 is approximated value =3.33, find the absolute and relative errors​

Answer 1

Step-by-step explanation:

If true value is equal to 10/3 is approximated value =3.33, find the absolute and relative errors

Answer 2

The absolute and relative errors are $\frac{1}{300}$ and $\frac{1}{1000}$.

Given:

The true value is equal to 10/3 and it is approximated to 3.33.

To Find:

The absolute and relative errors​.

Solution:

The absolute error is the magnitude of the difference between the true value and approximated value. It is given by,

${\rm Absolute\,\,\, Error}=|\rm approximated\,\, value-\rm true\,\, value|$

So, the absolute error for the given values is,

${\rm Absolute\,\,\, Error}=|3.33-\frac{10}{3}|\\=|\frac{9.99-10}{3}|\\=|\frac{-0.01}{3}|\\=\frac{1}{300}$

The relative error is the ratio of the absolute error and true value. It is given by,

${\rm Relative\,\,\, Error}=\frac{\rm Absolute\,\, error}{\rm True\,\, value}$

So, the  relative error for the given values is,

${\rm Relative\,\,\, Error}=\frac{\frac{1}{300} }{\frac{10}{3}}\\=\frac{1}{1000}$

Thus, the absolute and relative errors are $\frac{1}{300}$ and $\frac{1}{1000}$.