Chapter 7.3, Problem 64S

To determine

To Find:

Whether the given number is rational or irrational.

Answer to Problem 64S

Irrational

Explanation of Solution

Given:

Given number is :

3.787887888…

Concept Used:

• Rational number can be expressed as a ratio $\frac{a}{b}$ , where a and b are integers and b is not zero. The decimal form of a rational number is either a terminating or repeating decimal.
• The decimal form of an irrational number neither terminates nor repeats . Square roots of numbers that are not perfect square are irrational numbers.

Calculation:

  $\begin{array}{l}Given\\ 3.787887888\dots \\ \text{Clearly, }3.787887888\dots \\ \text{is a non-terminating , non-repeating decimal number }\text{.}\\ \text{So, by the definition of an irrational number , }3.787887888\dots \text{ is}\\ \text{an irrational number}\text{.}\end{array}$