Question

Is $1.5$ a rational number? Explain.

Answer 1

Hint: Here we have to show where the given decimal number is a rational number or not. Firstly we will write the definition of a rational number and what condition should be satisfied by a number to be a rational number. Then we will write the given decimal number into fraction form and see whether the condition is satisfied or not.

Complete step by step answer:
We have to show whether the below number is rational or not:
$1.5$….$\left( 1 \right)$
Rational numbers are those numbers whose decimal expansion is terminating or repeating. A number is said to be rational if it can be written in below form:
$\dfrac{p}{q}$
Where $p$ and $q$ both are integers and $q\ne 0$
Now we will write the number in equation (1) in fraction form by removing the decimal point from it and dividing the number by $10$ power equal to the digit after the decimal point.
 $\Rightarrow 1.5$
$\Rightarrow \dfrac{15}{{{10}^{1}}}$
We can write it as follows:
$\Rightarrow \dfrac{15}{10}$
We can see that the above value is expressed in $\dfrac{p}{q}$ form and both $15$ and $10$ are integers.
Hence $1.5$ is a rational number.

Note:
Rational numbers are one type of real numbers defined as a fraction with non-zero denominator. The rational numbers have terminating or repeating decimal expansion. This question can also be solved by the decimal expansion condition as we can see that the decimal number given is terminating, that is there is no sequence of infinite numbers after the decimal point. Rational numbers can be both positive as well as negative. When a number is not rational it is known as irrational numbers and their decimal expansion is non-terminating.