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Chapter 5: Problem 48

For Exercises \(47-58,\) identify the number as rational or irrational. $$-\frac{1}{9}$$

Short Answer

Expert verified
-\frac{1}{9} is a rational number.

Step by step solution

01

- Understand Rational and Irrational Numbers

Rational numbers are numbers that can be expressed as the fraction of two integers, where the denominator is not zero. Irrational numbers cannot be expressed as a simple fraction; they have non-repeating, non-terminating decimal parts.
02

- Analyze the Given Number

The given number is \(-\frac{1}{9}\). It is presented as a fraction where the numerator is \-1\ and the denominator is \9\.
03

- Determine if the Fraction Represents a Rational Number

Since \(-\frac{1}{9}\) is expressed as a fraction of two integers and the denominator is not zero, it is classified as a rational number.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction
A fraction represents a part of a whole. It is written in the form \(\frac{a}{b}\), where 'a' is the numerator (top part) and 'b' is the denominator (bottom part). The numerator indicates how many parts we have, while the denominator tells us into how many parts the whole is divided. For example, in the fraction \(\frac{1}{9}\), 1 is the numerator, showing we have one part, and 9 is the denominator, indicating the whole is divided into nine parts.
Fractions are a way to express numbers that are not whole, making them extremely useful in math and everyday life.
Integer
An integer is a whole number that can be positive, negative, or zero. It includes numbers like -2, -1, 0, 1, and 2. Integers do not have a fractional or decimal part. They can be visualized on a number line.
When dealing with fractions, both the numerator and the denominator should be integers. For example, in the fraction \(\frac{-1}{9}\), both -1 and 9 are integers. Knowing this helps us identify if a number is rational, as rational numbers are made from two integers.
Denominator
The denominator is the bottom number in a fraction. It indicates the total number of equal parts the whole is divided into. For instance, in the fraction \(\frac{1}{9}\), the denominator is 9, showing the whole is divided into nine equal parts.
The denominator must never be zero. If it is zero, the fraction is undefined because division by zero is undefined in mathematics. Always make sure to check the denominator when simplifying or converting fractions. In the given number \(-\frac{1}{9}\), the denominator is 9, a valid non-zero integer, confirming the number is rational.

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Most popular questions from this chapter

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