Numbers may be classified depending on their manner of representation or depending on the properties that they possess. Therefore, there are different types of numbers depending on the basis of classification. This is explained below.
MAIN TYPES
Natural Numbers: One of the main types of numbers is natural numbers, this refers to a group of counting numbers that are often referred to as natural numbers. The set of natural numbers is given by {1, 2, 3, 4, 5,
Whole Numbers: Whole numbers are a set of numbers that include natural numbers along with 0. The set of whole numbers is given by {0, 1, 2, 3, 4, 5,
Integers: They refer to a group of numbers including positive numbers, negative numbers, and also zero. That is, (…. -2, -1, 0, 1, 2
Rational numbers: This refers to all the numbers that are capable of being expressed in the ratio form of an integer to an integer that is non-zero. You should note that every integer is rational but it is not the same case for the converse. Examples include; 1/2, 3/4 and 1/5.
Irrational numbers: This refers to a group of real numbers that cannot be expressed as a ratio of two integers, such as √2, π, e.
Real numbers: This refers to a group of numbers that are capable of representing a distance along a line. All the numbers that can be represented on the number line, including rational and irrational numbers.
Complex numbers: Numbers that can be represented in the form of
NUMBER REPRESENTATIONS
Numbers can also be classified on the basis of how they are represented. Under this basis of classification, there are several groups. They are:
Decimals: This is a group of numbers that is represented using base ten. It is the standard numeral system for Hindu-Arabic. For example, 3.4, 45.76, 10.0
Binary: This refers to a numeral system that is used by computers. It is a numeral system of base two. For example, the binary number
Roman numerals: This refers to ancient Rome’s numeral system. You should note that up to today, it is still occasionally used. For example,
Fractions: This refers to a group of numbers that are represented as a ratio of 2 integers. This is inclusive of both mixed numbers and improper fractions. For example, \(3\frac{3}{2}\), \(\frac {1}{2}\)
Scientific notation: This refers to a method that is applied when writing very large or very small numbers by the use of powers of ten. For example, the speed of light is 3 × 108 meters per second.
SIGNED NUMBERS
Under this basis of classification, we have the following types:
Positive real numbers: These are real numbers that happen to be greater than zero.
Negative numbers: This refers to real numbers that happen to be less than zero.
Non-negative numbers: These are numbers that happen to be either greater than or equal to zero.
Non-positive numbers: This refers to real numbers that happen to be either equal to zero or less than zero.
TYPES OF INTEGER
Odd and even numbers: An integer is said to be even if it is a multiple of two. If not, it is said to be odd. For example, 4 is an even number and 9 is an odd number.
Prime number: This refers to a number that has exactly 2 divisors (positive), that is 1 and itself. For example, 5, and 7 are prime numbers.
Composite number: This is a number capable of being factored into smaller integers’ product. For example, 12 can be expressed as the product of 3 and 4.
In conclusion, numbers play a crucial role in mathematics and can be classified into different categories based on their properties and uses. Understanding the different types of numbers is crucial to solving mathematical problems and performing mathematical operations.
