Some Problems Question on Rational Numbers
Problem 1: Are the following statements true or false? Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
Answer 1:- (i) False, because zero is a whole number but not a natural number.
(ii) True, because every integer m can be expressed in the form m/1, and so it is a rational number.
(iii) False, because 3/5 is not an integer
Problem 2: Find five rational numbers between 1 and 2.
Answer 2:- Recall that to find a rational number between r and s, you can add r and s and divide the sum by 2, that is
r + s/2 lies between r and s. So, 3/2 is a number
between 1 and 2. You can proceed in this manner to find four more rational numbers between 1 and 2. These four numbers are
5/4, 11/8, 13/8, and 7/4.
Remark : Notice that in Example 2, you were asked to find five rational numbers between 1 and 2. But, you must have realised that in fact there are infinitely many rational numbers between 1 and 2. In general, there are infinitely many rational numbers between any two given rational numbers
Problem 3: Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?
Answer 3:- Yes Zero is a rational number and we write as 0/1 like p/q where p and q both are integer and q is not equal to 0.
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