Answered: 1) Give an example of a rational number…

Name: 1) Give an example of a rational number AND an irrational number.
Uploaded: 2024-03-20T06:38:44.000Z
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Description: 1) Give an example of a rational number AND an irrational number. What is the difference between them? 2) What is the decimal equivalent of your two examples? 3) Can every repeating decimal be written as a rational number? Explain why or why not

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1) Give an example of a rational number AND an irrational number.

What is the difference between them?

2) What is the decimal equivalent of your two examples?

3) Can every repeating decimal be written as a rational number? Explain why or why not.

Expert Solution

Step 1

(a)

A rational number is of the form $\frac{p}{q}$ where $p and q$ are integers where $q \neq 0$ .

The numbers that cannot be expressed in the form $\frac{p}{q}$ is called irrational numbers.

Example:

Rational number : $\frac{2}{5}$

Irrational number : $\sqrt{2}$

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