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Which numbers from the set [tex]\left\{-3,0,99.9,0.002,9,145, \frac{7}{8},-\frac{8}{9}\right\}[/tex] are rational?

A. [tex]-3,0,99.9,0.002,9,145, \frac{7}{8},-\frac{8}{9}[/tex]
B. [tex]0,9,145,99.9,0.002, \frac{7}{8}[/tex]
C. [tex]99.9,0.002, \frac{7}{8},-\frac{8}{9}[/tex]
D. [tex]-3,0,9,145[/tex]

Answer :

To solve this question, we need to identify which numbers in the given set are rational. A rational number can be expressed as the quotient of two integers, where the denominator is not zero.

Given set: [tex]\(\{-3, 0, 99.9, 0.002, 9, 145, \frac{7}{8}, -\frac{8}{9}\}\)[/tex]

Let's evaluate each number individually:

- -3: This is an integer, which can be written as [tex]\(\frac{-3}{1}\)[/tex]. It is a rational number.
- 0: This is an integer, which can be written as [tex]\(\frac{0}{1}\)[/tex]. It is a rational number.
- 99.9: This is a finite decimal, which can be expressed as [tex]\(\frac{999}{10}\)[/tex]. It is a rational number.
- 0.002: This is a finite decimal, which can be expressed as [tex]\(\frac{2}{1000} = \frac{1}{500}\)[/tex]. It is a rational number.
- 9: This is an integer, which can be written as [tex]\(\frac{9}{1}\)[/tex]. It is a rational number.
- 145: This is an integer, which can be written as [tex]\(\frac{145}{1}\)[/tex]. It is a rational number.
- [tex]\(\frac{7}{8}\)[/tex]: This is already in the form of a fraction with integer numerator and denominator. It is a rational number.
- [tex]\(-\frac{8}{9}\)[/tex]: This is already in the form of a fraction with integer numerator and denominator. It is a rational number.

Now, let's list all the identified rational numbers:

[tex]\[-3, 0, 99.9, 0.002, 9, 145, \frac{7}{8}, -\frac{8}{9}\][/tex]

Comparing this list with the options:

1. [tex]\(-3,0,99.9,0.002,9,145, \frac{7}{8}, -\frac{8}{9}\)[/tex]
2. [tex]\(0,9,145,99.9,0.002, \frac{7}{8}\)[/tex]
3. [tex]\(99.9,0.002, \frac{7}{8}, -\frac{8}{9}\)[/tex]
4. [tex]\(-3,0,9,145\)[/tex]

The correct option is:
[tex]\[-3, 0, 99.9, 0.002, 9, 145, \frac{7}{8}, -\frac{8}{9}\][/tex]

So, the correct choice is the first option:
[tex]\(\{-3, 0, 99.9, 0.002, 9, 145, \frac{7}{8}, -\frac{8}{9}\}\)[/tex].

Thanks for taking the time to read Which numbers from the set tex left 3 0 99 9 0 002 9 145 frac 7 8 frac 8 9 right tex are rational. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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