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  • State whether the given statement is true or false? Justify your answer by an example. Number of rational numbers between 15 and 18 is finite.

State whether the given statement is true or false? Justify your answer by an example. Number of rational numbers between 15 and 18 is finite.

Answers (1)

Answer: False

Solution.

Any number which can be represented in the form of p/q, where q is not equal to zero, is a rational number. So it is basically a fraction with non-zero denominator.
Examples: 4/5, 2/3, -6/7
So, it is a type of real number.
The given statement is: Number of rational numbers between 15 and 18 is finite.
If we see the definition of rational numbers as mentioned above, the given statement is false because between any two rational numbers, there exist infinitely many rational numbers.
Here, we have rational numbers between 15 and 18:
16,16.1\left ( =\frac{161}{10} \right ),16.2\left ( =\frac{162}{10} \right ),16.12\left ( =\frac{1612}{100} \right ),..... and infinitely more.
Therefore, the given statement is False.

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