Question

The number 8/7 = 1.14285714285714 ... obviously has no exact representation in any decimal floating point system (beta = 10) with finite precision t. Is there a finite floating point system (i.e., some finite integer base beta and precision t) in which this number does have an exact representation? If yes, then describe such a system. Answer the same question for the irrational number pi.

Answer 1

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the first point:

Yes, the Finite Floating Point Structures are considered  Where $\beta = 7$

$\to \frac{8}{7}= (1.1)_7$

$\bold{= 1 \times 7^0 + 1 \times 7^{-1}}$

In the second point:

There is no device with a finite floating-point since the right side is  

This equality never happens, then, with the rational numbers ($\alpha_i$ and $\beta$ is rational).