Question

A rational number between \[ - 3\] and \[3\] is
A. \[0\]
B. \[ - 4.3\]
C. \[ - 3.4\]
D. \[1.101100110001...\]

Answer 1

Hint: A rational number is the number represented in the form of \[\dfrac{p}{q}\] and here \[q \ne 0\] . A rational number should have a numerator and denominator.
In this question we are given with four options so we will check every option one by one that weather they are a rational number and if they lay between the range \[ - 3\] and \[3\] .The given options are in decimal form so we will convert them in fraction from and then will check for rational number.

Complete step-by-step answer:
A.Given the numbers between whom a rational number is to be find is \[ - 3\] and \[3\]
Now we will check all the options one by one
Given the number is \[0\] this can also be written as \[\dfrac{0}{0}\] , now we know for a rational number the number should be in \[\dfrac{p}{q}\] form and \[q \ne 0\] but here the \[q = 0\] , hence we can say \[0\] is not a rational number.

B.Given the number is \[ - 4.3\] this can also be written as
 \[ - 4.3 = - \dfrac{{43}}{{10}}\]
As we know for a rational number the number should be in \[\dfrac{p}{q}\] form and \[q \ne 0\] , hence we can say \[ - 4.3\] is a rational number but if we see the question we can say that \[ - 4.3\] does not lay in the range \[ - 3\] and \[3\] , hence \[ - 4.3\] is not a rational number between \[ - 3\] and \[3\] .

C.Given the number is \[ - 3.4\] this can also be written as
 \[ - 3.4 = - \dfrac{{34}}{{10}}\]
As we know for a rational number the number should be in \[\dfrac{p}{q}\] form and \[q \ne 0\] , hence we can say \[ - 4.3\] is a rational number but if we see the question we can say that \[ - 4.3\] does not lay in the range \[ - 3\] and \[3\] , hence \[ - 4.3\] is not a rational number between \[ - 3\] and \[3\] .

D.Given the number is \[1.101100110001\] this can also be written as
 \[1.101100110001 = \dfrac{{1101100110001}}{{1000000000000}}\]
As we know for a rational number the number should be in \[\dfrac{p}{q}\] form and \[q \ne 0\] , hence we can say \[1.101100110001\] is a rational number but if we see the question we can say that \[1.101100110001\] lay in the range \[ - 3\] and \[3\] , hence \[1.101100110001\] is a rational number between \[ - 3\] and \[3\] .
So, the correct answer is “Option D”.

Note: If the numbers a and b between whom a rational number is to be found is not equal then we can find the rational by using the formula \[\dfrac{{a + b}}{2}\] .
This gives a rational number between two unequal numbers.