Rational number
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 <math>\mathbb{Q}</math>, 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]
Fraction form[change]
All rational numbers can be written as a fraction. Take 1.5 as an example, this can be written as <math>1 \frac{1}{2}</math>, <math>\frac{3}{2}</math>, or <math>3/2</math>.
More examples of fractions that are rational numbers include <math>\frac{1}{7}</math>, <math>\frac{-8}{9}</math>, and <math>\frac{2}{5}</math>.
Terminating decimals[change]
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]
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 <math>\frac{1}{3}</math>. 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 <math>\frac{1}{11}</math>. 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 <math>\frac{1}{6}</math>. 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 <math>\frac{2}{3} = 0.6666667</math>, even though there is no 7. It rounds the 6 at the end up to 7.
Irrational numbers[change]
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]
- 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 <math>\frac{a}{b}</math> and <math>\frac{c}{d}</math> are equal if <math>ad = bc</math>.
Related pages[change]
References[change]
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-11.
- ↑ "Rational number". Encyclopedia Britannica. Retrieved 2020-08-11.
- ↑ Weisstein, Eric W. "Rational Number". mathworld.wolfram.com. Retrieved 2020-08-11.