Chapter 3.2, Problem 49IP

To determine

To estimates the value of the $\pi$ as $3.14$ and $\frac{22}{7}$ under certain cases.

Answer to Problem 49IP

The inequality for the value of $\pi$ is $3.141<\pi <3.143$ .

Explanation of Solution

Given information: Two estimates of $\pi$ are $3.14$ and $\frac{22}{7}$

Concept Used:

  $\pi$ is an irrational number where as $\frac{22}{7}$ is a rational number and is the approximation

of $\pi$ .

(a)

The graph of $\pi$ on the number line is:

  

The graph of $\pi$ upto seven places is 3.1428571and is shown above.

(b) The inequality for the value of $\pi$ is $3.141<\pi <3.143$

(c) $\pi$ is the ratio of the circumference to the diameter of the circle.

At the cases, where rotation is involved, concrete value for the problem is required, 3.14 is used instead of $\pi$ , which is a non-terminating value.