Compare & Order Real Numbers

Made of the set of rational and irrational numbers

Rational Numbers: can be written as a fraction (natural, whole, integer)

Irrational Numbers: can not be written as a fraction

You can compare and order real numbers by writing them in the same notation.

Write the numbers in decimal notation before comparing and ordering them.

 $\sqrt{7\ }\ \approx\ 2.645...$  

 $2\ \frac{2}{3}\ \approx\ 2.6666...$  

So  $\sqrt{7}\ <\ \ 2\ \frac{2}{3}$  

 $15.7\%\ \approx\ 0.157$  

 $\sqrt{0.02}\ \approx\ 0.141$  

 $So\ 15.7\%\ >\ \sqrt{0.02}$  

 $\sqrt{30}\approx5.48$  

 $6\ =\ 6$  

 $5\ \frac{4}{5}\ =\ 5.80$  

 $5.\overline{36}\ \approx5.37$  

 $From\ greatest\ to\ least\ \left\{5.\overline{36},\ \sqrt{30},\ 5\ \frac{4}{5},\ 6\right\}$