Question

All real numbers are rational numbers.
A True
B False

Answer 1

Hint: here we are asked if all real numbers are rational numbers or they are not while getting on the question one must know what are real numbers and what are rational numbers. The real numbers are those which we use daily they are integers negative or positive whole numbers and much more whereas the rational numbers are those numbers which can be expressed In the terms of \[\dfrac{p}{q}\] where \[p\] and q are integers and \[q\] cannot be equal to zero .

Complete step-by-step answer:
So in the question we are asked if all real numbers are rational numbers or not so numbers are of two broader categories that are real numbers and imaginary numbers. Real numbers are those numbers that we use in daily life; they can be integers, negative or positive whole numbers also.
Now rational numbers are those numbers only which can be expressed In the terms of \[\dfrac{p}{q}\] where \[p\] and q are integers and \[q\] cannot be equal to zero so as we can see real numbers include \[0\] also and the \[0\] cannot be expressed in the terms of \[\dfrac{p}{q}\] so all real numbers cannot be rational numbers. Hence All real numbers are rational numbers it is definitely false so option B False is the correct answer

Note: Here we say that all real numbers are not rational numbers also the numbers can be divided into two types real and imaginary numbers real numbers as we saw are those numbers that we use in daily life they can be integers, negative or positive whole numbers also.
And imaginary numbers are those numbers that can be expressed in the terms of the square root of a negative number(usually the square root of \[ - 1\] is represented by \[i\] or \[j\]. Further the real numbers can be divided into rational or irrational. As we saw earlier rational numbers are those numbers that can be expressed in the terms of \[\dfrac{p}{q}\]. Irrational numbers are those numbers which cannot be expressed in the terms of \[\dfrac{p}{q}\]. So rational numbers are a type of real numbers .