# Is 2.01 a rational, integer, natural, irrational?

Jun 26, 2015

So long as $2.01$ is an exact value and not an approximation, then it is a rational number, being equal to $\frac{201}{100}$.

It is not an integer, natural number or irrational.

#### Explanation:

Natural numbers are the numbers $0 , 1 , 2 , 3 , \ldots$ or $1 , 2 , 3 , \ldots$. Some definitions include $0$ and some don't.

Integers are whole numbers or negative versions of them, that is: $0 , 1 , - 1 , 2 , - 2 , 3 , - 3 , \ldots$

Rational numbers are 'fractions' of integers. That is they are all the numbers of the form $\frac{p}{q}$ where $p$ and $q$ are both integers and $q \ne 0$.

Irrational numbers are numbers which are not rational, that is they are not expressible as $\frac{p}{q}$ for some integers $p$ and $q$ with $q \ne 0$.

$2.01$ is rational because $2.01 = \frac{201}{100}$ and both of $201$ and $100$ are integers.