**SUMMARY**

The most basic type of number is the

**natural or counting number.**These numbers are learned as toddlers and include all positive whole numbers.

**Whole numbers**are a larger set that includes natural numbers and zero.

**Integers**are an even larger set that consists of all whole numbers and the negatives of natural numbers. While all-natural and whole numbers are integers, not all integers are natural or whole numbers.

**Rational numbers**can be written as a fraction, where the numerator and denominator are whole numbers, and the denominator cannot be zero. All

**fractions**are rational numbers, but not all rational numbers are fractions. The word "rational" comes from the word "ratio", as these numbers are ratios of two integers.

**Irrational numbers**cannot be written as a fraction and include numbers such as pi and the square root of 2.

**Real numbers**are the set of all rational and irrational numbers. All integers are real numbers, but not all real numbers are integers. Real numbers include whole numbers, fractions, repeating and terminating decimals, and more.

Number classification is a fundamental concept in Mathematics that involves **grouping or categorising numbers based on their properties and characteristics.** This concept helps to organise and understand different types of numbers and their relationships, leading to a deeper understanding of mathematical concepts and their applications.

There are different ways of classifying numbers, including prime, composite, rational, irrational, natural, whole, integers, and real numbers. Each category has unique properties; understanding them is crucial in solving mathematical problems and real-world applications.

**Prime Numbers:**Prime numbers are positive integers greater than 1 that have no positive integer divisors other than 1 and itself. For example, prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37.

Prime numbers have several important properties. For instance, they cannot be expressed as a product of two smaller positive integers. This property makes prime numbers useful in cryptography and coding theory, where they are used to create secure codes and passwords.

**Composite Numbers**: Composite numbers are positive integers that have at least one positive divisor other than 1 and itself. For example, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, and 21 are composite numbers.

Composite numbers have several properties that make them useful in mathematics. For instance, they can be expressed as a product of prime factors. This property is important in factorisation problems and finding common denominators in fractions.

**Rational Numbers:**Rational numbers can be expressed as a ratio of two integers where the denominator is not zero. For example, 3/4, 5/8, -2/3, and 1 are rational numbers.

Rational numbers have several properties, including the fact that they can be expressed as either terminating or repeating decimals. This property is important in converting fractions to decimals and vice versa.

**Irrational Numbers:**Irrational numbers cannot be expressed as a ratio of two integers. They are non-repeating and non-terminating decimals. For example, √2, √3, and π are irrational numbers.

Irrational numbers have several properties, including that they cannot be expressed as a fraction and have an infinite number of non-repeating decimal places. This property is important in calculus and other advanced mathematical fields.

**Natural Numbers:**Natural numbers are counting numbers that start from 1 and go to infinity. For example, natural numbers are 1, 2, 3, 4, 5, and so on.

Natural numbers have several properties that make them useful in mathematics. For instance, they can represent quantities, such as the number of items in a set or the number of people in a group.

**Whole Numbers:**Whole numbers are natural numbers and zero. For example, whole numbers are 0, 1, 2, 3, 4, etc.

Whole numbers have several properties that make them useful in mathematics. For instance, they can represent values like game scores or length measurements.

**Integers:**Integers are whole numbers and their negative counterparts. For example, -3, -2, -1, 0, 1, 2, and 3 are integers.

Integers have several properties that make them useful in mathematics. For instance, they can represent values, such as temperatures or positions on a number line.

**Real Numbers:**Real numbers can be represented on a number line. They include both rational and irrational

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