Number Systems and Classification

Number Systems

• Natural Numbers: Positive whole numbers (1, 2, 3, ...)
• Whole Numbers: Non-negative whole numbers (0, 1, 2, ...) - Includes natural and zero.
• Integers: Positive and negative whole numbers. (..., -3, -2, -1, 0, 1, 2, 3, ...) - Includes whole numbers and negatives.
• Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. - Includes terminating and repeating decimals.
• Irrational Numbers: Numbers that cannot be expressed as a fraction and have non-terminating and non-repeating decimals. - Examples include π (pi) and the square root of 2.

Real Numbers

• Real numbers include all rational and irrational numbers.

Prime and Composite Numbers

• Prime Numbers: Whole numbers greater than 1 that have only two factors: 1 and themselves. Examples: 2, 3, 5, 7.
• Composite Numbers: Whole numbers greater than 1 that have more than two factors.

Decimal Types

• Terminating Decimals: Decimals that end after a finite number of digits. Examples: 0.5, 2.75, 1.2
• Repeating Decimals: Decimals that have a repeating pattern of digits. Examples: 0.333..., 0.121212...

Non-Terminating and Non-Repeating Decimals

• These decimals represent irrational numbers. Examples include π and √2.

Factorization

• Factorization is the process of breaking down a number into smaller numbers that multiply to the original number.