Question

Every rational number is a real number. State whether the given statement is true or false. Justify.

Answer 1

Hint: In this type of question we just need to know the basics of the number system and definitions of real number and rational number is must to solve this question, after knowing definitions of above mentioned terms one must observe that a given statement is true or false.

Complete step by step answer:
To check if the above given statement is true or false we must know first the basic definition of Real numbers and rational numbers of the number system.
So below is the definition of Real Numbers:
Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. At the same time, the imaginary numbers are the un-real numbers, which cannot be expressed in the number line and is commonly used to represent a complex number.
Example - \[0,1,-1,2,5.\overline{3},\dfrac{1}{6}\] , etc.
As the above definition clearly says that real numbers consist of rational numbers, but apart from definition we will look after the concept or we can say definition of rational numbers and then we will see how they can be a subset of real numbers.
First we will see the definition of rational numbers:
In Maths, rational numbers are represented in \[\dfrac{p}{q}\] form where \[q\] is not equal to zero. It is also a type of real number. Any fraction with non-zero denominators is a rational number. Hence, we can say that \['0'\] is also a rational number, as we can represent it in many forms such as \[\dfrac{0}{1},\dfrac{0}{2},\dfrac{0}{3},\] etc. But, \[\dfrac{1}{0},\dfrac{2}{0},\dfrac{3}{0},\] etc. are not rational, since they give us infinite values. Also, check irrational numbers here and compare them with rational numerals.
As we noticed above by seeing the definition of rational numbers that rational numbers are ratio of two integers and the numbers which are terminating after decimal point or non-terminating but repeating can be represent in the form of rational numbers, therefore we can conclude two statements:
First, every real number cannot be represented as rational numbers.
Second is every rational number is a representation of a real number.
Therefore, the given statement that is “Every rational number is a real number” is TRUE.
Therefore our final answer is TRUE.

Note: The rational numbers can be seen as a fraction and it is widely being used everywhere in day to day life as when we want to share any whole thing then we use this concept, they are used in many industries and banks to calculate interest and loans and in many more problems.