Question

A rational number between \[ - \dfrac{2}{3}\]and \[\dfrac{1}{2}\]?

A) \[ - \dfrac{3}{6}\]
B) \[ - \dfrac{1}{{12}}\]
C) \[ - \dfrac{5}{6}\]
D) \[\dfrac{5}{6}\]

Answer 1

Hint: Here as from the options we need to check which are rational numbers lying between \[ - \dfrac{2}{3}\] and \[\dfrac{1}{2}\], hence we first find the decimal representation of the given numbers and then check whether they are rational or not, if they are rational then we check whether they lie between \[ - \dfrac{2}{3}\] and \[\dfrac{1}{2}\]. If a number satisfies both the condition then that number is the required answer.

Complete step by step solution: The given rational number are \[ - \dfrac{2}{3}\] and \[\dfrac{1}{2}\]

Hence, the approximate value of the given rational numbers are

\[
   - \dfrac{2}{3} = - 0.67 \\
  \dfrac{1}{2} = 0.5 \\
 \]

Hence, we have to select the value which lies between \[( - 0.67,0.5)\]

Checking for option (C) and (D).

Hence, as the value of \[\dfrac{{ - 5}}{6},\dfrac{5}{6}\]will be around \[ - 0.83,0.83\].

As both the values don’t lie between \[( - 0.67,0.5)\].

Hence, both this option will be eliminated.

Checking for option (B)

And the value of \[ - \dfrac{1}{{12}} = - 0.083333\],

As, the value don’t lie between \[( - 0.67,0.5)\],

Hence, this option will be eliminated.

Option (A) is \[ - \dfrac{3}{6} = - 0.5\], as this lies between \[( - 0.67,0.5)\].

Hence, option (A) will be our required answer.

Note: A rational number is a number that can be expressed as the quotient or fraction \[\dfrac{p}{q}\] of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed in that way is irrational.