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Number System (Assignment #1)

Total: 12 points

1. Consider the numbers [tex]$500, 0.11, -9, \sqrt{5}, \frac{22}{7}, \frac{1}{10}, 0$[/tex] and categorize them in the following sets of numbers:

a.) Natural numbers: [tex]$\quad \_\_\_\_\_\_\_\_\_\_\_\_\_$[/tex]
[10 points]

b.) Whole numbers: [tex]$\quad \_\_\_\_\_\_\_\_\_\_\_\_\_$[/tex]

c.) Integers: [tex]$\quad \_\_\_\_\_\_\_\_\_\_\_\_\_$[/tex]

d.) Rational numbers: [tex]$\quad \_\_\_\_\_\_\_\_\_\_\_\_\_$[/tex]

e.) Irrational numbers: [tex]$\quad \_\_\_\_\_\_\_\_\_\_\_\_\_$[/tex]

f.) Real numbers: [tex]$\quad \_\_\_\_\_\_\_\_\_\_\_\_\_$[/tex]

Sagot :

GinnyAnswer
To categorize the given numbers 500, 0.11, -9, [tex]\(\sqrt{5}\)[/tex], [tex]\(\frac{22}{7}\)[/tex], [tex]\(\frac{1}{10}\)[/tex], and 0 into different sets, let's go through each set step-by-step:

### a) Natural Numbers

Natural numbers are positive integers starting from 1 and going upwards (1, 2, 3, ...). Among the given numbers, only 500 is a positive integer fitting this category.

- Natural Numbers: [tex]\(\{500\}\)[/tex]

### b) Whole Numbers

Whole numbers include all natural numbers along with zero (0, 1, 2, 3, ...).

- Whole Numbers: [tex]\(\{0, 500\}\)[/tex]

### c) Integers

Integers include all positive and negative whole numbers along with zero (... -3, -2, -1, 0, 1, 2, 3 ...). Among the given numbers, 500, -9, and 0 fit this category.

- Integers: [tex]\(\{0, -9, 500\}\)[/tex]

### d) Rational Numbers

Rational numbers are numbers that can be expressed as a fraction or ratio of two integers (including terminating and repeating decimals). Among the given numbers, the following fit this category: 0, 0.11, -9, 500, [tex]\(\frac{22}{7}\)[/tex], [tex]\(\frac{1}{10}\)[/tex].

- Rational Numbers: [tex]\(\{0, 0.11, -9, 500, \frac{22}{7}, \frac{1}{10}\}\)[/tex]

### e) Irrational Numbers

Irrational numbers cannot be expressed as a simple fraction; their decimal expansions are non-repeating and non-terminating. Among the given numbers, [tex]\(\sqrt{5}\)[/tex] fits this category.

- Irrational Numbers: [tex]\(\{\sqrt{5}\}\)[/tex]

### f) Real Numbers

Real numbers include all rational and irrational numbers. In this case, all the given numbers are real numbers.

- Real Numbers: [tex]\(\{0, 0.11, -9, 500, \sqrt{5}, \frac{22}{7}, \frac{1}{10}\}\)[/tex]

To summarize, the categorizations are:

- a) Natural Numbers: [tex]\(\{500\}\)[/tex]
- b) Whole Numbers: [tex]\(\{0, 500\}\)[/tex]
- c) Integers: [tex]\(\{0, -9, 500\}\)[/tex]
- d) Rational Numbers: [tex]\(\{0, 0.11, -9, 500, 3.142857142857143, 0.1\}\)[/tex]
- e) Irrational Numbers: [tex]\(\{2.23606797749979\}\)[/tex]
- f) Real Numbers: [tex]\(\{0, 0.11, -9, 500, 2.23606797749979, 3.142857142857143, 0.1\}\)[/tex]
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