# Absolute and Relative Errors : Three-Digit Chopping and Rounding Arithmetic

Please help with the following problems. Provide step by step calculations.

Compute the absolute error and the relative error in approximations of p by p*.

a) p = pi , p* = 22/7

Perform the the following computations i) exactly, ii) using three-digit chopping arithmetic, iii) using three digit rounding arithmetic.

iv) Compute the relative errors in parts ii) and iii).

(1/3 - 3/11) + 3/20

https://brainmass.com/math/computing-values-of-functions/absolute-relative-errors-three-digit-chopping-rounding-arithmetic-103703

#### Solution Preview

Problem #1 Compute the absolute error and the relative error in approximations of p by p*.

a) p = pi , p* = 22/7

When we talk about the absolute error and relative error, we need to define how accurate we want. In this problem, p=pi, p*=22/7. Let us use the 4-digit rounding algorithm.

Then, p=pi=3.14159=3.1416 with error <=0.00001. ...

#### Solution Summary

Absolute and Relative Errors and Three-Digit Chopping and Rounding Arithmetic are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question. Step by step calculations are provided.