Answers/Step-by-step explanation:
First, let's define the different categories that real numbers can be grouped into:
Naturals. These are the numbers that can be used to both count and order things There numbers can't be negatives. Examples: 1, 2, 3, 4, 5.
Whole numbers. Just like natural numbers, but include 0. Examples: 0, 1, 2, 3, 4, 5.
Integers. These are the numbers that can be written without the need to use a fractional component. They are formed by negative numbers, positive numbers, and 0. Examples: -1, 5, 0, -42.
Rational numbers. These are numbers that can be expressed as a fraction of integers. Examples: 1/2, 4/5, -1/3, -5/9.
Irrational numbers (real algebraics). There are the numbers tnat can't be expressed as the fraction of two integers. Examples: [tex]\pi[/tex], [tex]\sqrt{45}[/tex], [tex]1-\sqrt{2}[/tex].
Check attached image 1 to better understand the classification of numbers.
Now let's solve the exercises.
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Name the set or sets of numbers to which each real number belongs.
1. [tex]-\sqrt{64} =-8[/tex]: Integer, rational.
2. [tex]\frac{8}{3}[/tex]: Rational.
3. [tex]\sqrt{28}[/tex]: Irrational.
4.[tex]\frac{56}{7} =8[/tex]: Natural, whole, integer, rational.
5. [tex]-\sqrt{22}[/tex]: Irrational.
6.[tex]\frac{36}{6}[/tex]: Natural, whole, integer, rational.
7. [tex]-\frac{5}{12}[/tex]: Rational.
8. [tex]\frac{18}{3}=6[/tex]: Natural, whole, integer, rational.
9. [tex]\sqrt{10.24}=3.2[/tex]: Rational.
10. [tex]-\frac{54}{19}[/tex]: Rational.
11. [tex]\sqrt{\frac{82}{20} }[/tex]: Irrational.
12. [tex]\frac{72}{8}=9[/tex]: Natural, whole, integer, rational.
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Graph each set of numbers on a number line. Then order the numbers from leaft to greatest.
For this exercise, I'll digitally graph the numbers for you on a cartesian plane so you can draw the number line and order them. Check attched image 2 to see how a number line should look like.
Check atached image 3, 4 and 5 to see each group of numbers organized in the number line.
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Learn more about the classification of numbers and ordering numbers on the number line here:
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