Question

List five rational numbers between -2 and -1.

Answer 1

Hint: The given interval is -2 and -1. We have that a rational number must be of the form \[\dfrac{p}{q}\] and we have one restriction on a denominator that is, it must not be equal to zero. In this case, \[q\] is the denominator so, \[q\] must not be equal to zero, \[q\ne 0\] . Also, every terminating decimal point number is a rational number. Now, pick any five terminating decimal point numbers between -2 and -1.

Complete step by step answer:
According to the question, we are given an interval of the rational numbers and we have to pick five rational numbers between them.
The given interval is \[\left( -2,-1 \right)\] . That is, we have to pick any five rational numbers between the interval -2 and -1.
We have that a rational number must be of the form \[\dfrac{p}{q}\] and we have one restriction on a denominator that is, it must not be equal to zero. In this case, \[q\] is the denominator so, \[q\] must not be equal to zero, \[q\ne 0\] . Also, every terminating decimal point number is a rational number.
Since we have to pick any five rational numbers between the interval -2 and -1, and we can pick decimal point numbers. So, we have to pick out any five decimal point numbers between -2.00 and \[-1.00\].
The five decimal point numbers can be -1.2, -1.3, -1.4, -1.5, and -1.6.
Hence, the five rational numbers between -2 and -1 are -1.2, -1.3, -1.4, -1.5, and -1.6.

Note:
For solving this type of question, just go with the basic definition of the rational number. That is, a rational number is a number which must be of the form \[\dfrac{p}{q}\] such that \[q\ne 0\]. Also, every terminating decimal point number is a rational number.