Types of Numbers - Hun Kim Tutorials

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Give examples of the following types of numbers:
1. Natural
  Solution
  $1, 2, 3, ...$
2. Whole
  Solution
  $0, 1, 2, 3, ...$
3. Integers
  Solution
  $..., -3, -2, -1, 0, 1, 2, 3, ...$
4. Rational
  Solution
  Numbers that can be expressed in the form $\frac{a}{b}$ where $a$ and $b$ are integers
5. Real
  Solution
  Includes all rational number but also irrational numbers such as $\sqrt{2}, \pi, e$
6. Complex
  Solution
  Is a combination of real numbers and imaginary number for example $3+i$ which means $3+\sqrt{-1}$
Rational or irrational?
1. $\sqrt{5}$
  Solution
  Irrational
2. $\sqrt{\frac{25}{9}}$
  Solution
  Rational
3. $\pi$
  Solution
  Irrational
4. $1.\bar{6}$
  Solution
  Rational
What letter symbols represents the types of numbers?
1. Natural
  Solution
  $\mathbb{N}$
2. Whole
  Solution
  $\mathbb{W}$
3. Integer
  Solution
  $\mathbb{Z}$
4. Rational
  Solution
  $\mathbb{Q}$
5. Real
  Solution
  $\mathbb{R}$
6. Complex
  Solution
  $\mathbb{C}$
Which of the following are irrational numbers?
- I: $\pi$
- II: $2.5234872983123 ...$
- III: $1.5$
- IV: $2.\bar{3}$
- V: $\sqrt{2}$
- VI: $\sqrt{16}$
  Solution
  Choices I, II, V
Rank from least to greatest:
- I: $2.5$
- II: $\sqrt{9}$
- III: $-100$
- IV: $3\sqrt{2}$
- V: $\frac{8}{3}$
- VI: $3.\bar{3}$
- VII: $\infty$
- VIII: $200%$
  Solution
  III, VIII, I, V, II, VI, IV, VII
List the first four prime numbers
Solution
$2, 3, 5, 7$
List the first four perfect squares
Solution
$1, 4, 9, 16$
List the first four positive perfect cubes
Solution
$1, 4, 9, 16$
Challenge: Show that $1.\bar{23}$ is a rational number
Solution
Let $x=0.\bar{23}$
Then $100x=23.\bar{23}$
Subtract these two equations
$99x=23$
$x=\frac{23}{99}$