Rational number

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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.

Writing rational numbers[change | edit source]

Fraction form[change | edit source]

All rational numbers can be written as a fraction. Take 1.5 as an example. This can be written as 1 \frac{1}{2}, \frac{3}{2}, or 3/2.

More examples of fractions that are rational numbers include \frac{1}{7}, \frac{-8}{9}, and \frac{2}{5}.

Terminating decimals[change | edit 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 | edit source]

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 \frac{1}{3}. 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 \frac{1}{11}. 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 \frac{1}{6}. 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 \frac{2}{3} = 0.6666667, even though there is no 7. It rounds the 6 at the end up to 7.

Irrational numbers[change | edit 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 | edit 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 \frac{a}{b} and \frac{c}{d} are equal if ad =  bc.

Other pages[change | edit source]