Summary: Classes of Real Numbers

Key Concepts

  • Real numbers
The image shows a large rectangle labeled “Real Numbers”. The rectangle is split in half vertically. The right half is labeled “Irrational Numbers”. The left half is labeled “Rational Numbers” and contains three concentric rectangles. The outer most rectangle is labeled “Integers”, the next rectangle is “Whole Numbers” and the inner most rectangle is “Natural Numbers”.

The Order of Operations

  • Perform all operations within grouping symbols first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.
  • Evaluate exponents or square roots.
  • Multiply or divide, from left to right.
  • Add or subtract, from left to right.

This order of operations is true for all real numbers.


Irrational number
A number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
Rational number
A number that can be written in the form [latex]{\Large\frac{p}{q}}[/latex] , where p and q are integers and [latex]q\ne 0[/latex] . Its decimal form stops or repeats.
Real number:
A number that is either rational or irrational.