First, we'll need to convert [tex]\frac{-83}{7}[/tex] and [tex]-\sqrt{133}[/tex] into numbers that are easier to work with for ordering:
[tex]\frac{-83}{7}=-11\frac{6}{7}[/tex]
[tex]-\sqrt{133}=-11.5[/tex]
Then in order from least to greatest, we would want:
[tex]\frac{-83}{7},-11.6,-\sqrt{133},11\frac{5}{10}[/tex]
Real numbers are all rational and irrational numbers. Rational numbers are numbers which can be expressed as a fraction which means that they would eventually contain a repeating sequence in their decimal expansion (decimal form). Irrational numbers are numbers which cannot be expressed as fractions, examples often include [tex]\pi, \sqrt{2}[/tex], as there is no way to write these numbers exactly as fractions.
