# Is the number 1 rational or irrational?

Rational

#### Explanation:

A rational number is one that can be expressed as a fraction of integers. For instance, we can express the number 1 in an infinite number of ways:

$\frac{1}{1} , \frac{2}{2} , \frac{3}{3} , \frac{- 1}{- 1}$

In fact, any integer divided by itself will give us 1.

An irrational number is one that cannot be expressed as a fraction of two integers. For instance, the most famous of irrational numbers is $\pi$ - the ratio of a circle's circumference to its diameter. As an approximation, $\pi$ is sometimes expressed as $3.14$ or $\frac{22}{7}$, but in actuality the decimal runs forever, never repeating and never ending.

Dec 26, 2016

The number 1 can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer.

This is only possible because $1$ is a RATIONAL number.

#### Explanation:

Once a number is irrational, that's it. It cannot be classified further.

However,$\textcolor{m a \ge n t a}{\text{ rational}}$ numbers can be classified into different types of numbers.

A rational number is defined as 'A number which can be written in the form $\textcolor{m a \ge n t a}{\frac{p}{q}}$ where $p \mathmr{and} q$ are integers, but $q \ne 0$

Some rational numbers become integers, some remain as fractions:

Integers:$\frac{30}{5} , \frac{12}{4} , - \frac{9}{3} , \textcolor{m a \ge n t a}{\frac{7}{7}} , \frac{0}{8}$ Fractions: $\frac{2}{3} , \frac{15}{4} , \frac{1}{7}$

Some integers are negative, the rest are whole numbers.

Whole numbers include $\left\{0 , \textcolor{m a \ge n t a}{1} , 2 , 3 , 4 , 5 , 6 , \ldots \ldots\right\}$

Whole numbers can be broken down into 0 and natural numbers.

Natural numbers include {color(magenta)(1)(,2,3,4,5,6...}

Within the natural numbers you will also have different types of numbers, including odds, evens, primes, composites, perfect squares, perfect cubes, etc.

The number $\textcolor{m a \ge n t a}{1}$ can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer.

This is only possible because it is a rational number.

Note that $\textcolor{m a \ge n t a}{1}$ is not prime because it has only one factor.