Chapter SH, Problem 10.2.7EP

To determine

The name of number as whole, integer, rational or irrational number.

  $\mathrm{5.14726...}$

Answer to Problem 10.2.7EP

The $\mathrm{5.14726...}$ number is irrational number.

Explanation of Solution

Given:

Number: $\mathrm{5.14726...}$

Concept Used:

Whole Number: A whole number is number without fractions.

Integer: Integer is a number which not a fraction.

Rational Number: Rational number can be expressed as the quotient or fraction of two integers. Since one number is rational number.

As by the definition the rational number if two numbers are $p$ and $q$ then one of them such as $q$ is rational number.

Decimal part of rational numbers is either terminated or repeated infinitely.

So, the number $\mathrm{5.14726...}$ has non repeated decimal expansion.

It cannot be written as $\frac{p}{q},q\ne 0$

Conclusion:

Hence, the $\mathrm{5.14726...}$ number isirrational number.