Question

By managing to refine a well-known measuring technique, you find a value of pi equal to 3.141. How much absolute error is there in this calculation? Relative Error? Percent Error? (I really need an explanation i know how to do all of these formulas, but my answers keep coming out wrong?? Please, I really need some help. I’m freaking out)

Answer 1

We know that the true value for pi is given as 3.14156.

Now, we have been given that the approximate value for pi is 3.141

We know the formula

Absolute error,
`\Delta x = | \text{True value } - \text{ Approximate value} | \\ \\ \Delta x =|3.14156-3.141|\\ \\ \Delta x =0.00056`

Relative error is given by

`\text{Relative error }= \frac{\Delta x}{\text{true value} }\\ \\ \text{Relative error }=(0.00056)/(3.14156) \\ \\ [tex]\text{Relative error }=0.000178`

The percentage error is given by

`\text{Relative error } * 100\\   \\   0.000178* 100   \\   =0.0178 \%`