Chapter 6.6, Problem 6WE

a.

To determine

whether the given number is rational or irrational

Answer to Problem 6WE

The given number is rational number

Explanation of Solution

Given information :

Given number is 75.4682

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

The given number 75.4682 can definitely be represented in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$ . Hence we can conclude that this number is rational number

b.

To determine

whether the given number is rational or irrational

Answer to Problem 6WE

The given number is rational number

Explanation of Solution

Given information :

Given number is $75.\overline{4682}$

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

The given number can be written as $75.\overline{4682}=\frac{754682-75}{9999}=\frac{754607}{9999}$

The given number is represented in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$ .

Hence we can conclude that this number is rational number

c.

To determine

whether the given number is rational or irrational

Answer to Problem 6WE

The given number is an irrational number

Explanation of Solution

Given information :

Given number is 75.468244682444682…

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

The given number (75.468244682444682…) cannot be represented in the form $\frac{p}{q}$ where $p$ and $q$ are integers. This particular given number has infinite non repeating decimal digits. Hence we can conclude that this number is rational number.