A value that represents a quantity along a continuous number line is called a real number. They are a combination of rational numbers and irrational numbers. Integers, natural numbers, negative numbers, whole numbers, etc., are real numbers. Imaginary numbers cannot be represented on a number line, and therefore, they do not fall under the types of real numbers.
Around 1000 BC, simple fractions were used by Egyptians. Early Indian Mathematicians such as Manava (750 – 690 BC) accepted the concept of irrationality. They found that square roots of certain numbers such as 2 could not be determined precisely. The importance of the square root of 2 was also realized by Greek Mathematicians led by Pythagoras.
Indian and Chinese Mathematicians accepted concepts of zero, negative numbers, fractional numbers, and integers during the middle ages. Arabic Mathematicians eventually merged all these numbers into one topic called real numbers. As research progressed further, the concept of real numbers developed into what we know them as today.
Types of Real Numbers
Real numbers can be classified as follows:
Numbers that cannot be written in the form of p/q and are not rational numbers are called irrational numbers. They are non-terminating and non-repeating. An example of an irrational number is 2.
Numbers that can be expressed in the form of p/q wherein q is not equal to 0. Rational numbers can be positive or negative. They are terminating or non-terminating and repeating decimals. Examples are 0.3333, 0.25 etc.
Fractions fall under the category of rational numbers. All fractional numbers are rational numbers, but all rational numbers are not fractions. A fraction is any number that can be expressed in the form a/b where a and b are whole numbers, and b is not equal to 0.
Integers also fall under the category of rational numbers. Whole numbers and all negative natural numbers make up integers.
Numbers that are below zero are called negative numbers. They fall under the category of integers.
These numbers also fall under the category of integers and consist of all-natural numbers and zero.
All counting numbers that start from one are called natural numbers.
Properties of Real Numbers
The properties of real numbers are as follows
The numbers can be moved from their position without changing the final answer. This property can be applied to addition and multiplication. If a and b are two numbers then according to this property a+b = b+a and a.b = b.a
Regardless of the grouping of numbers, you can add and multiply them without altering the result. If we have three numbers a,b,c then according to this property a+(b+c) = (a+b)+c and a.(b.c) = (a.b).c
If you multiply the sum of two or more numbers, the result should be the same as multiplying each number individually by the said number and adding their sum. Let a,b,c be three numbers then a.(b+c) = a.b+a.c
If a number is multiplied by 1, you get the same number, i.e., a.1=a. Also, if zero is added to the number, it stays the same. a + 0 = a. This is the identity property.
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