Question

Insert three rational numbers between -2 and -1.

Answer 1

Hint: To solve such a question it is important to know first what are rational numbers. Rational numbers are any number which can be written as a form of \[\dfrac{p}{q}\] where p can be any number but q is non zero.

Complete Step-by-Step solution:
In this question we have to insert three rational numbers between -2 and -1.
This can be done by taking a number which is in between -2 and -1 that is we will try to get a number which is greater than -2 but at the same time is less than -1. Any number which is of the form \[\dfrac{p}{q}\] is a rational number where q is nonzero.
Then obviously all integers are also rational numbers where q is nothing but 1.
But we do not have any integer in between -2 and -1, therefore we can only assume rational numbers where the denominator q is not equal to one.
Any number which is in between -1 and -2 would be of the form -1.1, -1.2 and -1.3 and so on.
We select three of these numbers as -1.4, -1.5 and -1.6.
Now we try to convert all these selected numbers in the form of \[\dfrac{p}{q}\], so that we can get them in original rational number form.
We have,
\[-1.4=\dfrac{-14}{10}=\dfrac{-7}{5}\]
And \[-1.5=\dfrac{-15}{10}=\dfrac{-3}{2}\]
And finally, \[-1.6=\dfrac{-16}{10}=\dfrac{-8}{5}\].
Hence, we obtain three rational numbers in between -1 and -2 as \[\dfrac{-7}{5},\dfrac{-3}{2},\dfrac{-8}{5}\], which is the required result.

Note: Always while calculating the answer of the question where we have to insert 3 rational number, convert the obtained integer point value in rational \[\dfrac{p}{q}\], where q is non zero, so that we can get the answer as originally formed rational number.