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:
$$a)\hspace{.1em}\sqrt{18}$$
$$b)\hspace{.1em}\sqrt{15}$$
