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State whether the following statement is true or false. Give reason for your answer.
Every rational number is a whole number.___
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Question

State whether the following statement is true or false. Give reason for your answer.
Every rational number is a whole number.___

Answer

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Solution

As we know, a rational number is the one that can be written in the form of \(\frac{p}{q},\) where \(q \neq 0\)
As we know, whole number is \(0,1,2,3,4,5 \ldots\)
Now, we know, every number can be written in the form of \(\frac{p}{q},\) we get
\(\frac{0}{1}, \frac{1}{1}, \frac{2}{1}, \frac{3}{1}, \frac{4}{1}, \frac{5}{1}\)
Here, we can see that every whole number is a rational number.
But, every rational number \(\left(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}\right)\) is not a whole number as whole numbers are free from decimals and fraction.
Therefore, not every rational number is a whole number. But, every whole number is a rational number.
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