Compare & Order Real Numbers

Compare & Order Real Numbers

The Real Number System

• 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

Open Ended

Name all sets of numbers to which each real number belongs.

 $\sqrt{36}$  

Open Ended

Name all sets of numbers to which each real number belongs.

0.2525...

Open Ended

Name all sets of numbers to which each real number belongs.

 $-2\ \frac{2}{5}$  

Compare & Order Real Numbers

• 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.

Compare

 $\sqrt{7}$   and  $2\ \frac{2}{3}$  

•  $\sqrt{7\ }\ \approx\ 2.645...$  

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

• So  $\sqrt{7}\ <\ \ 2\ \frac{2}{3}$  

Compare  $15.7\%\ and\ \sqrt{0.02}$  

•  $15.7\%\ \approx\ 0.157$  

•  $\sqrt{0.02}\ \approx\ 0.141$  

•  $So\ 15.7\%\ >\ \sqrt{0.02}$  
  

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

Order the set from least to greatest. 

•  $\sqrt{30}\approx5.48$  

•  $6\ =\ 6$  

•  $5\ \frac{4}{5}\ =\ 5.80$  

•  $5.\overline{36}\ \approx5.37$  

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

Open Ended

Name all sets to which the real number belongs...

 $-\sqrt{64}$  

Open Ended

Name all sets to which the real number belongs...

 $\sqrt{17}$  

Multiple Choice

Which makes the number sentence true?

 $\sqrt{15}\ \ \ \ \ \ \ \ 3.5$  

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Multiple Choice

Which makes the number sentence true?

 $\sqrt{2.25}\ \ \ \ \ \ \ \ \ \ \ 150\%$  

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Open Ended

Order the set from least to greatest.

 $\left\{\sqrt{5},\ 220\%,\ 2.25,\ 2.\overline{2}\right\}$  

Questions

Does anyone have any questions on comparing and ordering real numbers?

Remember to convert each number to a decimal and it will be easy to compare them!