Chapter 6.6, Problem 29WE

To determine

To find a rational number and an irrational number between the given pair.

Answer to Problem 29WE

Rational number $=0.8755$

Irrational number $=\mathrm{0.875287522875222...}$

Explanation of Solution

Given information :

Given pair is $\frac{7}{8}$ and $\frac{8}{9}$

Rational numbers: rational number are those numbers which can be represented in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$

Irrational numbers: these are the numbers which cannot be written as simple fraction and are non-termination and non-repeating numbers. For example $\sqrt{2}=\mathrm{1.41421356....}$

Now we are given a pair of number and we have to find rational and irrational number between them. However there are many rational and irrational numbers between the given pair, but we will mention two of them here.

The value of $\frac{7}{8}=0.875$ and $\frac{8}{9}=\mathrm{0.8888...}$

Rational number $=0.8755$ (we may take any number that can be represented in fraction with integers between the given range.)

Irrational number $=\mathrm{0.875287522875222...}$ (we may take any non-termination, non-repeating number that cannot be represented into simple fraction between the given range.)