Chapter SH, Problem 10.2.9EP

To determine

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

  $\mathrm{0.3535...}$

Answer to Problem 10.2.9EP

The $\mathrm{0.3535...}$ number is rational number.

Explanation of Solution

Given:

Number: $\mathrm{0.3535...}$

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 whole number is nothing but the integer and the integer is nothing but the number without fraction.

The rational number if two numbers are $p$ and $q$ then one of them such as $q$ is rational number.

Decimal part of the rational number is either terminated or repeated infinitely.

So, the given number is $\mathrm{0.3535...}$ and it is rational number.

It has the repeated decimal.

This number can be written as $\mathrm{0.3535...}=\frac{35}{99}$

  $\mathrm{0.3535...}$ is a rational number.

Conclusion:

Hence, the $\mathrm{0.3535...}$ number is rational number.