All About Types of Numbers

A number is an arithmetic value used to indicate the quantity of an object in mathematics. We use numbers in our daily lives to count money, time, and objects, among other things. In the number system, we have various types of numbers. In this post, we’ll look at the many sorts of numbers in math, as well as their qualities and examples.

Types of Numbers in Maths

The numbers are categorised into distinct sorts based on their qualities and how they are represented on the number line. Each number categorization has a description, attributes, and examples to help you understand it better.

The following are the various types of numbers:

Natural Numbers

Natural numbers, often known as counting numbers, are the most basic types of numbers that you learned as a toddler. They go from 1 to infinity, for example, 1, 2, 3, 4, 5, 6, and so on. Positive integers are another name for them. They can be written as follows in set form:

{1, 2, 3, 4, 5, …}

The symbol N is used to indicate natural numbers.

Whole Numbers

The set of natural numbers that includes zero is known as whole numbers. This means they start at 0 and work their way up to 1, 2, 3, and so on.

{0, 1, 2, 3, 4, 5, …}

The sign W is used to denote whole numbers.

Integers

The collection of all whole numbers and natural number negatives is known as integers. They include any numbers that fall between negative and positive infinity. They can be positive, zero, or negative, but not in decimal or fractional form. Set form for integers is as follows:

{…, -3, -2, -1, 0, 1, 2, 3, …}

While all whole numbers and natural numbers are integers, not all integers are whole numbers or natural numbers.

Integers are represented by the letter Z.

Fractions

Parts of a full piece are represented by fractions. It can be represented as a/b, where a and b are both whole numbers, and b can never equal 0. Not all rational numbers are fractions, but all fractions are rational numbers.

Proper and improper fractions are separated from fractions. Proper functions, on the other hand, have the denominator greater than the numerator, and improper fractions have the numerator greater than the denominator. Proper fractions include 3/7 and 99/101, while improper fractions include 7/3 and 101/99. This means that the improper fractions are never less than 1.

Fractions can be written for all terminating and repeating decimals. The terminating decimal 1.25 can be written as 125/100 = 5/4. The decimal fraction 0.3333 can be represented as 1/3.

Rational Numbers

In fraction form, you can write rational numbers. The word “rational” comes from the word “ratio,” because rational numbers are the ratios of two integers. For example, because it can be expressed as 7/10, 0.7 is a rational number. Other rational numbers are -1/3, 2/5, 99/100, 1.57, and so on.

Consider p/q, a rational number with two numbers p and q. Because the fraction is indeterminate, the numerator p can be any integer (positive or negative), while the denominator q can never be 0. If q = 1, the fraction is also an integer.

The letter Q stands for rational numbers.

Irrational Numbers

Irrational numbers can’t be represented in fraction form, which means they can’t be expressed as the ratio of two integers. √2, √5, 0.353535…, and so on are examples of irrational numbers. The digits in irrational numbers can be seen to continue indefinitely with no pattern.

Irrational numbers are represented by the letter Q.

Real Numbers

The set of all rational and irrational numbers is known as real numbers. All numbers that can be written in decimal form are included. Not all real numbers are integers, and not all integers are real numbers. All integers, whole numbers, fractions, repeating decimals, terminating decimals, and other real numbers are included.

The letter R stands for real numbers.

Imaginary Numbers

Imaginary or complex numbers are numbers that are not real. When we square an imaginary number, the result is negative, indicating that it is the square root of a negative number, such as -2 and -5. The squared values of these numbers are -2 and -5. The letter I stands for the square root of the negative one.

Examples include √2, i2, 3i, etc.and others.

Imaginary Numbers’ Properties:

The feature of Imaginary Numbers is intriguing. When doing a multiplication operation, it cycles through four different numbers each time.

1 × I =I

I × I = -1

-1 × I = -i

-i × I = 1

As a result, the imaginary numbers can be written as: i = √1

i2 = -1

i3 = -i

i4 = +1

i4n = 1

i4n-1= -i

Example 1: Using pre-number math skills, assist Ron in completing the number counting chain.

1, _, _, _, 5, _, _, _, _, 10.

Solution:

Ron must watch the pattern of numbers in order to complete the number counting chain. It begins at 1 and concludes at 10. The following is the complete number chain:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Example 2: Sort the following integers into even and odd categories: 1, 3, 4, 7, 12, 21, 29, 32

Solution:

Even numbers are those that are divisible by two exactly. Even numbers are 4, 12, and 32, but odd numbers are those that are not divisible by two. As a result, the numbers 1, 3, 7, 21, and 29 are odd.

Conclusion

Numbers are crucial. Costs, sales, performance, and targets are all figures that most people believe are significant. The ability to interpret these metrics is critical; they can influence judgments about performance, investments, and efficacy, among other things.