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Question

Write, whether the given statement is true or false. Give reasons.
(i) Every natural number is a whole number.
(ii) Every whole number is a natural number.
(iii) Every integer is a rational number.
(iv) Every rational number is a whole number.
(v) Every terminating decimal is a rational number.
(vi) 0 is a rational number.


Solution

(i) True
Natural numbers start from 1 to infinity and whole numbers start from 0 to infinity; hence, every natural number is a whole number.

(ii) False
0 is a whole number but not a natural number, so every whole number is not a natural number.

(iii) True
Every integer can be expressed in the pq form.

(iv) False
Because whole numbers consist only of numbers of the form p1, where p is a positive number. On the other hand, rational numbers are the numbers whose denominator can be anything except 0.

(v) True
Every terminating decimal can be easily expressed in the pq form.

(vi) True
Every terminating decimal can be easily expressed in the pq form.

(vii) True
0 can be expressed in the form pq, so it is a rational number.

Mathematics
RS Aggarwal (2017)
Standard IX

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