Question

Is $0.25$ a rational number?

Answer 1

Hint: Rational numbers are the numbers that can be written in the form of a fraction where numerator and denominator are integers. Rational numbers are written in the form of $\dfrac{p}{q}$ where $(q \ne 0)$. For example, $\dfrac{2}{3}$ is a rational number as it is in the form of $\dfrac{p}{q}$ where $(q \ne 0)$.

Complete step by step answer:
In the question we need to determine if $0.25$ is a rational number or not. Rational numbers are the numbers that can be written in the form of a fraction. In the case of rational numbers, numerator and denominator should be coprime and the denominator should not be equal to zero.

Coprimes are the numbers that have only $1$ as a common factor. For example, $3$ and $10$ are coprimes because the only common factor between them is $1$.So check $0.25$ is a rational number by writing it in the form of $\dfrac{p}{q}$ where $(q \ne 0)$.We can write $0.25$ as $\dfrac{{25}}{{100}}$.

For removing decimal we divide the numerator by $100$ as after decimal there are two numbers so we divide $25$ by $100$. Now, $\dfrac{{25}}{{100}}$ can be written as $\dfrac{1}{4}$. Hence, $\dfrac{1}{4}$ is a rational number as it is in the form of $\dfrac{p}{q}$ where $(q \ne 0)$. Therefore, $.25$ is a rational number as it can be written in the form $\dfrac{1}{4}$ which is a rational number and also the numerator and denominator are coprimes.

Hence, $0.25$ is a rational number.

Note: We are able to write $.25$ in fraction as it is the terminating decimal number.A terminating decimal is a decimal that has an end. If it is a non-terminating decimal which has no end we can’t write it in fraction. If we can’t write it in fraction we can’t term it as a rational number. For a decimal to be a rational number it should be a terminating decimal.