Rational number

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In mathematics, a rational number is a number that can be written as a fraction. The set of rational number is often represented by the symbol , standing for "quotient" in English.[1] [2]

Rational numbers are all real numbers, and can be positive or negative. A number that is not rational is called irrational.[3]

Most of the numbers that people use in everyday life are rational. These include fractions, integers and numbers with finite decimal digits. In general, a number that can be written as a fraction while it is in its own form is rational.

Writing rational numbers[change | change source]

Fraction form[change | change source]

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[change | change source]

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[change | change source]

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

An example of this is . As a decimal, it is written as 0.3333333333... The dots indicate that the digit 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[change | change source]

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[change | change source]

  • 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 .

Related pages[change | change source]

References[change | change source]

  1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-11.
  2. "Rational number". Encyclopedia Britannica. Retrieved 2020-08-11.
  3. Weisstein, Eric W. "Rational Number". mathworld.wolfram.com. Retrieved 2020-08-11.