### About Classifying Real Numbers:

When we work with the real number system, each real number can be labeled as a "rational number" or an "irrational number". We can further break down some rational numbers into other categories such as an "integer", "whole number", or "natural number".

Test Objectives

- Demonstrate the ability to determine if a number is a Natural Number
- Demonstrate the ability to determine if a number is a Whole Number
- Demonstrate the ability to determine if a number is an Integer
- Demonstrate the ability to determine if a number is a Rational Number
- Demonstrate the ability to determine if a number is an Irrational Number

#1:

Instructions: How can we classify the given number?

$$a)\hspace{.1em}-2$$

$$b)\hspace{.1em}-\frac{4}{3}$$

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#2:

Instructions: How can we classify the given number?

$$a)\hspace{.1em}\sqrt{4}$$

$$b)\hspace{.1em}\frac{\sqrt{5}}{1}$$

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#3:

Instructions: How can we classify the given number?

$$a)\hspace{.1em}0.\overline{45}$$

$$b)\hspace{.1em}\frac{\sqrt{13}}{2}$$

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#4:

Instructions: Determine which of the following numbers are Whole Numbers.

$$a)\hspace{.1em}-8, \frac{14}{2}, \sqrt{36}$$

$$b)\hspace{.1em}\sqrt{60}, \frac{-8}{-1}, -12 $$

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#5:

Instructions: Determine which of the following numbers are Irrational Numbers.

$$a)\hspace{.1em}-\sqrt{81}, -1.6\overline{321}, \sqrt{18}$$

$$b)-90, -\sqrt[3]{27}, \sqrt{15}$$

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Written Solutions:

#1:

Solutions:

a) Integer, Rational Number

b) Rational Number

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#2:

Solutions:

a) Natural Number, Whole Number, Integer, Rational Number

b) Irrational Number

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#3:

Solutions:

a) Rational Number

b) Irrational Number

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#4:

Solutions:

$$a)\hspace{.1em}\frac{14}{2}:(7), \sqrt{36}:(6)$$

$$b)\hspace{.1em}\frac{-8}{-1}: (8)$$

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#5:

Solutions:

$$a)\hspace{.1em} \sqrt{18}$$

$$b)\hspace{.1em} \sqrt{15}$$