Question

Is $\dfrac{2}{3}$ a rational number?

Answer 1

Hint: All those numbers which are non-terminating and non-repeating are irrational numbers. But if we convert this fraction into decimal numbers, we will see that the number is repeating. There is one more identification of a rational number by checking whether the number present in numerator and denominator are integers or not.

Complete step-by-step answer:
In the given question, we know that
The numbers present in the denominator are both integers and we know that if a number that can be written as a ratio of two integers, of which the denominator is non-zero, is a rational number.
In general, we can say that a rational number can be expressed as $\dfrac{p}{q}$, where p and q are integers and q is not zero.
Therefore, $\dfrac{2}{3}$ is a rational number.
Also,
We can say that the value of $\dfrac{2}{3}$ is equal to $0.66666$, which is a non-terminating and repeating value and we know that the values which are non-terminating and repeating are rational numbers.
So, from this definition also we can say that $\dfrac{2}{3}$ is a rational number.

Note: A number is rational if we can write it as a fraction, where both denominator and numerator are integers and the denominator is a non-zero number. The standard form of a rational number can be defined if it’s no common factors aside from one between the dividend and divisor and therefore the divisor is positive. For example, \[\dfrac{{12}}{{36}}\] is a rational number. But it can be simplified as $\dfrac{1}{3}$; common factors between the divisor and dividend are only one. So, we can say that the rational number $\dfrac{1}{3}$ is in standard form.