 # Rational Numbers

## Rational Numbers Definition:

A rational number is a number that can be expressed as a fraction p/q of two Integers, a numerator p and a non-zero denominator q.

## Rational Numbers Notation

We represent the set of Rational Numbers as ℚ
Rational Numbers extend from but do not include (-∞, ∞)

## What do Rational Numbers Include?

Natural (Counting) Numbers (ℕ) (1, 2, 3, 4, ...). Since every natural number can be written as itself divided by 1
Whole Numbers (0, 1, 2, 3, 4, ...) Since every whole number can be written as itself divided by 1
Negative Counting Numbers (..., -4, -3, -2, -1) Since every negative counting number can be written as itself divided by 1
Fractions (3/5, -4/7)
Decimals (2.4, -8.1)

## What do Rational Numbers NOT Include?

Positive Infinity ∞
Negative Infinity -∞
Imaginary Numbers like i = √-1

## Properties of Rational Numbers

Positive Rational Numbers are to the right of 0 on a number line
Negative Rational Numbers are to the left of 0 on a number line
As we move right on the number line, Rational Numbers increase in value
As we move left on the number line, Rational Numbers decrease in value
Extend infinitely (but do not include infinity)
Any non-zero Rational Numbers is either negative or positive.

## Rational Numbers Calculator:

To see if a number is an Rational Numbers, you can ask the search engine questions like is 15 a Rational Number

### How does the Rational Numbers Calculator work?

This lesson walks you through what rational numbers are, how to write rational numbers, rational number notation, and what‘s included in rational numbers

### What 3 formulas are used for the Rational Numbers Calculator?

1. Rational Numbers are written in the form p/q where q is non zero
2. We represent the set of Rational Numbers as ℚ
3. Rational Numbers extend from but do not include (-∞, ∞)

For more math formulas, check out our Formula Dossier

### What 6 concepts are covered in the Rational Numbers Calculator?

natural number
the positive integers (whole numbers)
1, 2, 3, ...
number
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
property
an attribute, quality, or characteristic of something
rational number
a number that can be expressed as the quotient or fraction p/q of two integers
rational numbers
whole number
numbers that include natural numbers and zero
{0, 1, 2, 3, ...}