Question

Is \[\dfrac{1}{2}\] a real and rational number?

Answer 1

Hint: A real number is a value of a continuous quantity that can represent a distance along a line. Real numbers are the numbers which include both the rational numbers and as well as irrational numbers. 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 non-zero denominator $q$ .
For example, $ - \dfrac{3}{7}$ is a rational number , as is every integer. i.e., $\mathbb{Q}$ is the set of all rational numbers in the form $\mathbb{Q} = \left\{ {\dfrac{a}{b}:a,b \in \mathbb{Z}{\text{ and b}} \ne {\text{0}}} \right\}$

Complete answer:
Real numbers are the numbers which include both rational and irrational numbers. Rational numbers such as integers $1, - 3,0,5,6....$ , fractions like $\dfrac{2}{3},\dfrac{5}{2},.....$ and irrational number such as $\sqrt 3 ,\pi ,..etc.$, are all real numbers.
Real numbers are numbers that can be placed on a number line and rational numbers are numbers that can be written as a fraction, therefore $\dfrac{1}{2}$ meets both of these conditions.
Therefore $\dfrac{1}{2}$ is a real and rational number.

Note:
Students also remember that the definition of a real number is also a rational number. By the other hand, $\mathbb{R}$ is a superset containing $\mathbb{Q}$ , it’s say $\mathbb{Q} \subset \mathbb{R}$ , That means whichever element of $\mathbb{Q}$ is also a element of $\mathbb{R}$ and $\dfrac{a}{b}$ is also real number , where $a,b \in \mathbb{Z}$ and $b \ne 0$ .