Rational Numbers

A value is a Rational Number if it can be expressed as an Integer divided by an integer.

Any Integer a can be expressed as \dfrac{a}{1} so every integer is a rational number.

A decimal is a finite decimal if the decimal numbers stop at some point. Any finite decimal can be expressed as a rational number using the following trick:

  • Write the a fraction with the decimal in the numerator and the value “1” in the denominator.
  • Multiply the top and bottom values of the fraction by 10, as many times as it takes to convert the numerator from a decimal into an integer.

Example:

We can convert 3.14159 to an integer divided by an integer using the above procedure.

\dfrac{3.14159}{1} = \dfrac{31.4159}{10} = \dfrac{314.159}{100} = \dfrac{3141.59}{1000} = = \dfrac{31415.9}{10000} = \dfrac{314159}{100000}

There is one more class of rational numbers. Some decimals numbers that have an infinite number of decimals, follow a repeating pattern and they can be expressed as an integer divided by an integer.

For example, 0.33333… with the 3’s repeating forever, can be expressed as \dfrac {1}{3}.

Additional Reading Below…