Chapter 4.7, Problem 20IP

To determine

To Write the name of all sets to which each real number belongs.

Answer to Problem 20IP

  $\mathrm{0.55555......}$ is a number which belongs to the set of rational number.

Explanation of Solution

Given information:

The number is $\mathrm{0.55555......}$ .

Calculation:

A rational number is a number which can be written in $\frac{p}{q}$ form where $p$ and $q$ are integers and $q\ne 0$ .

An irrational number is a number which cannot be written in $\frac{p}{q}$ form.

An integer is a whole number which can be positive, negative or zero.

A natural number consists of all counting numbers.

A whole number consists of all counting numbers including $0$ .

  $\mathrm{0.55555......}=0.\overline{5}$ is a terminating and repeating decimal number which belongs to the set of rational number.