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# Rational number

In mathematics, a **rational number** is a number that can be written as a fraction. Rational numbers are all real numbers, and can be positive or negative. A number that is not rational is called irrational.

Most of the numbers that people use in everyday life are rational. These include fractions and integers.

## Contents

## Writing rational numbers

### Fraction form

All rational numbers can be written as a fraction. Take 1.5 as an example. This can be written as , , or .

More examples of fractions that are rational numbers include , , and .

### Terminating decimals

A terminating decimal is a decimal with a certain number of digits to the right of the decimal point. Examples include 3.2, 4.075, and -300.12002. All of these are rational. Another good example would be 0.9582938472938498234.

### Repeating decimals

A repeating decimal is a decimal where there are infinitely many digits to the right of the decimal point, but they follow a repeating pattern.

An example of this is . As a decimal, it is written as 0.3333333333... The dots tell you that the number **3** repeats forever.

Sometimes, a group of digits repeats. An example is . As a decimal, it is written as 0.09090909... In this example, the group of digits **09** repeats.

Also, sometimes the digits repeat *after* another group of digits. An example is . It is written as 0.16666666... In this example, the digit **6** repeats, following the digit 1.

If you try this on your calculator, sometimes it may make a rounding error at the end. For instance, your calculator may say that , even though there is no 7. It rounds the 6 at the end up to 7.

## Irrational numbers

The digits after the decimal point in an irrational number do not repeat in an infinite pattern. For instance, the first several digits of π (Pi) are 3.1415926535... A few of the digits repeat, but they never start repeating in an infinite pattern, no matter how far you go to the right of the decimal point.

## Arithmetic

- Whenever you add or subtract two rational numbers, you always get another rational number.

- Whenever you multiply two rational numbers, you always get another rational number.

- Whenever you divide two rational numbers, you always get another rational number, as long as you do not divide by zero.

- Two rational numbers and are equal if .

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