BGCSE CORE
TYPES OF NUMBERS

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REal numbers can be classified into several categories:
Rational Numbers: numbers that can be written as a fraction where both the numerator and denominator are integers.

Irrational Numbers: numbers that CANNOT be written as fractions. For example, pi and root 2. If we try to write these numbers as decimals they go on forever, with no recurring digits.

Rational Numbers CAN be expressed as a quotient of two numbers (a fraction)

Irrational Numbers CANNOT be expressed as a quotient of two numbers (a fraction)

Whole Numbers: counting numbers starting at zero. They are not negative. EXAMPLES: 0, 4, 21, 145, 2000
Natural Numbers: also called counting numbers. They are whole numbers greater than zero. They are not negative. EXAMPLES: 1, 5, 15, 215, 6204 Integers: are whole numbers, both negative and positive, including zero.EXAMPLES: 3, 2, 1, 0, 1, 2, 3, …. Even Numbers: counting numbers that are divisible by 2. These end in 2, 4, 6, 8, 0. EXAMPLES: 256, 58, 25000, 352 Odd Numbers: counting numbers that are not divisible by 2. These end in 1, 3, 5, 7, 9. EXAMPLES: 29, 681, 4425 
Square Numbers: integers written as the product of an integer multiplied by itself. EXAMPLES: 4 (2x2), 16 (4x4), 144 (12x12), 81 (9x9), 10000 (100x100)
Cube Numbers: integers written as the product of an integer multiplied by the square of itself. EXAMPLES: 8 (2x2x2), 27 (3x3x3), 125 (5x5x5), 1000 (10X10X10) Triangular Numbers: numbers formed by adding consecutive integers starting with 1. They form triangles when dots are used. (1, 1+2, 1+2+3…) EXAMPLES: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55... Surds: Surds are numbers left in the form √n where n is a positive integer that is not a square number. Prime Numbers: numbers greater than 1 that have only two factors: 1 and the number itself. 2 is the first and only even prime number. Factors: one of two numbers, which when multiplied, give you a product. Multiples: the result of multiplying two whole numbers. 