Real Number Systems

Natural numbers are the set of positive integers starting from 1, 2, 3, and so on. They do not include zero or negative numbers.

Whole numbers are the set of non-negative integers, including zero. They are 0, 1, 2, 3, and so on.

Integers are the set of whole numbers that include positive numbers, negative numbers, and zero. Examples: -3, -2, -1, 0, 1, 2, 3.

Rational numbers are numbers that can be expressed as a fraction $$\frac{a}{b}$$ , where $$a$$ and $$b$$ are integers and $$b \neq 0$$ . Examples: 1/2, -3, 0.75.

Irrational numbers are numbers that cannot be expressed as a simple fraction. Their decimal representation is non-repeating and non-terminating. Examples: $$\sqrt{2}$$ , $$\pi$$ .

$$\sqrt{121} = 11$$ , which is a natural number, whole number, integer, and rational number.

-7.5 is a rational number because it can be expressed as $$\frac{-75}{10}$$ .

Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. Example: 564,000,000 = 5.64 x 10^8.

To convert a large number to scientific notation, move the decimal point to create a number between 1 and 10, then count the number of places moved to determine the exponent of 10.

Rational numbers and irrational numbers are mutually exclusive sets. Rational numbers can be expressed as fractions, while irrational numbers cannot.