Question

let denote the machine epsilon in our idealized decimal machine, which uses chopping instead of rounding in its calculations. if we enter , the output would be 1 eps.

Answer 1

The machine epsilon is the smallest positive number that can be represented in a decimal machine. It represents the difference between 1 and the next largest number that can be represented.

Step-by-step explanation:

The machine epsilon, denoted as ε, is the smallest positive number that can be represented in a given floating-point format. In the idealized decimal machine that uses chopping, the machine epsilon represents the difference between 1 and the next largest number that can be represented. For example, if we enter 1 + ε in this machine, the output would be 1, since chopping would eliminate any digits beyond the machine epsilon.

For instance, if the machine epsilon is 0.0001, then 1 + 0.0001 would be chopped down to 1. The machine epsilon determines the precision of calculations in the decimal machine.