Question

Find the five rational numbers between \[\dfrac{1}{2}\]and\[\dfrac{3}{2}\].
A. \[0.5 < 0.6 < 0.7 < 0.8... < 1.1 < ... < 1.15 < 1.50\]
B. \[0.5 < 0.6 < 1.7 < 0.8... < 1.1 < ... < 1.15 < 1.50\]
C. \[0.5 < 0.6 < 0.7 < 2.8... < 1.1 < ... < 1.15 < 1.50\]
D. \[0.5 < 0.6 < 0.7 < 0.8... < 3.1 < ... < 1.15 < 1.50\]

Answer 1

Hint: Rational number is any number that can be denoted in the form of\[\dfrac{p}{q}\], where\[q \ne 0\] and this\[\dfrac{p}{q}\]can further be simplified and expressed in form of decimal value. Rational Numbers include all the positive and negative integers including \[0\] because all the integers can be expressed in the said form. To solve the given question in a simplified manner, we will first convert both the given values in decimal form and check from the options if the values given are or not between \[\dfrac{1}{2}\]and\[\dfrac{3}{2}\]

Complete step-by-step answer:
At first, convert both the given numbers in decimal form.
\[\dfrac{1}{2}\]can be expressed as\[0.5\], and,
\[\dfrac{3}{2}\]can be expressed as, \[1.5\]
Hence, it can be said that five rational numbers between\[\dfrac{1}{2}\] and\[\dfrac{3}{2}\] should be greater than\[0.5\] and less than\[1.5\].
Now, we will check one-by-one the given options if values are between\[0.5\]and\[1.5\],
For option (A), \[0.5 < 0.6 < 0.7 < 0.8... < 1.1 < ... < 1.15 < 1.50\]
All the values are between \[0.5\]and\[1.5\]and in the correct order.
For option (B), \[0.5 < 0.6 < 1.7 < 0.8... < 1.1 < ... < 1.15 < 1.50\]
In this option, \[1.7\]is given which is greater than\[1.5\].
For option (C), \[0.5 < 0.6 < 0.7 < 2.8... < 1.1 < ... < 1.15 < 1.50\]
In this option, \[2.8\]is given which is greater than\[1.5\].
For option (D), \[0.5 < 0.6 < 0.7 < 0.8... < 3.1 < ... < 1.15 < 1.50\]
In this option, \[3.1\] is given which is greater than\[1.5\].

So, the correct answer is “Option A”.

Note: It is important to understand that there are far more than five numbers between\[\dfrac{1}{2}\]and\[\dfrac{3}{2}\]
We can insert an infinite number of rational numbers between them. If the options were not given in the above question, clearly we could add as many as numbers between \[0.5\]and\[1.5\].
If the common factor between \[p,q\]is only \[1\], then the rational number\[\dfrac{p}{q}\] is said to be in its standard form.