Question

Between $\mathrm{1.7320508...}$ and $\mathrm{0.333...}$, which is the rational and which is the irrational number?

• A. Both are irrational numbers
• B. $\mathrm{1.7320508...}$ is irrational number, while $\mathrm{0.333...}$ is rational number
• C. Both are rational numbers
• D. None of the above

Answer 1

The correct option is B $\mathrm{1.7320508...}$ is irrational number, while $\mathrm{0.333...}$ is rational number

A rational number is a number that can be written in the form of $\frac{p}{q}$, where $p,q$ belong to the set of integers and $q$ is not equal to $0$.
All numbers except non- terminating
and non-repeating numbers can be written in this form.

$\therefore$ $\mathrm{1.7320508...}$, a non-terminating, non-repeating number is an Irrational Number.

$\mathrm{0.333..}$ is a non-terminating but repeating number that can be written in the form of $\frac{p}{q}$, where $p,q$ belong to the set of integers and $q$ is not equal to $0$, making it a Rational Number.