# Is 7/6 a irrational number?

Mar 30, 2016

$\frac{7}{6}$ is not irrational

#### Explanation:

As $\frac{7}{6}$ is a fraction, it is a rational number and not irrational number. Irrational numbers cannot be written as a fraction or ratio of two integers.

Rational numbers, when expressed in decimal form have either terminating decimals (when denominator of the fraction in its smallest form has only $2$ and $5$ as prime factors) on non-terminating but repeating decimals.

If a number written in decimal form has non-terminating as well as non-repeating decimals, then it cannot be written as a ratio of two integers and is hence irrational.

As $\frac{7}{6} = 1.16161616 \ldots \ldots .$, in which $16$ get repeated (till infinity), it can be expressed as a fraction and is not irrational.