Question

Discuss whether the following statements are true or false, provide reasons in the support of your answer.

• Every integer is a rational number and vice versa.
• Every decimal number can be represented as a rational number.

Answer 1

Any rational number can be written in the form of p/q, where p and q are integers, and q is nonzero. So, any integer can be written in the form of p/q.
For example, 2 =
2/1.
Take any rational number in the simplest form, whose denominator is not either 1 or -1.
For example; ⅔ , is it an integer?
no.
So, the given statement is false.

Next statement, every decimal number can be represented as a rational number.
It’s true.
For example, 1.23 = 1 + 2/10 + 3/100 = 123/100
So, you can write any decimal number as a rational number.