What Is a Real Number?

A real number is a number that can be found on the number line which means all the numbers that we use and apply in real-world are real numbers. There are many types of real numbers:
Natural numbers: Any counting number is a natural number and it starts from 1. On the number line, these are located from the right after 0. The smallest natural number is 1. Examples: 1, 2, 178, 289, etc.
Whole numbers: A whole number is also a counting number but can also include 0. It starts from the right of the number line and 0 is the smallest whole number. Ex: 0, 122, 456 67890, etc.
Integers: An integer is a whole number and can also its negative numbers. An integer can be a positive integer or a negative integer. 0 is also an integer.
Positive integers start from 1 and are plotted from the right of the number line. They are counting or natural numbers. Ex: 1,2, 3, 5678, etc.
Negative integers: These start from -1 and are found left of the number line and before 0. These are negative whole numbers. Ex: -1, -234, -5678
Fractions: These are written between integers and is part of a whole number. Ex:½, 2/2, etc.
Rational and irrational numbers: A Rational number is a number that is a ratio of two integers. These can be a natural number, whole number, fraction or an integer. Ex: -⅛, 5 ¾, etc.
An irrational number is a number that cannot be broken into a ratio of two integers. Ex: 0, e, π, etc.

The real number line: A geometric line with an ‘origin’ is called a real number line. The Points that are to the right of the origin is positive numbers and to the left is negative.  The distance between the two points is chosen to be 1.

Properties Of A Real Number:
Commutative property: The real numbers are like any other numbers and basic mathematical operations like addition, subtraction, multiplication, and division can be done. The order of numbers is not important. Ex: 1+2 = 2+1
Distributive property: Multiplication of numbers distributes across addition. Ex: 3 • (4 + 5) = 3 • 4 + 3 • 5
Associative property: Regrouping of elements can be done without moving the location of the number. Ex: 4 + (3 + 5) = (4 + 3) + 5
Symmetric property: Numbers that are equal can be read forward or backwards producing the same result. Ex: a = b then b = a
Infinite real numbers: Since the whole numbers are a subset of the real numbers, these are uncountable.
Infinity and imaginary numbers like the square root of -1 is not a real number.

Real-Life Application Of Real Numbers
1. It helps in counting the different items in a grocery store or calculate the amount to be paid.
2. In work-place, you use it in accounting, finance or publishing reports.
3. Flicking TV channels from one to another or directly inputting the channel number which is a real number.
4. Calling someone from your phone using the phone number is also using real numbers.
5. Calculating the speed or measuring the distance and time
6. Checking the temperature, wind speed, etc.
7. Car driving dashboard