Question

State true or false:
Every rational number is a whole number.
(a) True
(b) False

Answer 1

Hint:In this question, we first need to look at the basic definitions of number system. Then from the definitions of rational numbers and whole numbers we can conclude whether the given statement is true or false.

Complete step-by-step answer:
NUMBER: A number tells us how many times a unit is contained in a given quantity.
NATURAL NUMBERS: Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.
$$N=\{1,2,3......\}$$
WHOLE NUMBERS: The system of Natural numbers along with number 0, is called whole number and is denoted by W.
$$W=\{0,1,2,3......\}$$
INTEGERS: Any number having sign '+' or '-' without having any fractional part is called integer (including zero).
$$Z=\{.....,-3,-2,-1,0,1,2,3,....\}$$
RATIONAL NUMBERS: A number which can be written in the form of $${\displaystyle \frac{p}{q}}$$ , where $$p,q\in Z$$ and $$q\ne 0$$, is called rational number. A rational number can be expressed as decimal.
Whole number is a positive number without a fraction or decimal. But, a rational number is any number that can be expressed as a fraction.
Thus, every rational number is not a whole number.
Hence, the correct option is (b).

Note:For example if we consider 2.5 then it can be expressed as $${\displaystyle \frac{5}{2}}$$. So , it is a rational number but not the whole number. Then if we consider 5 then it can be expressed as $${\displaystyle \frac{5}{1}}$$ . So, it is both a rational number and whole number. Hence, every rational number is not a whole number but every whole number can be expressed as a rational number.