rational vs. irrational numbers

Rational vs. Irrational Numbers

Today I will determine if numbers are rational or irrational based on certain criteria.

Rational Numbers

• Numbers that can be written as a fraction

• Numbers that can be written as a terminating or repeating decimals

• The square roots of perfect squares

Multiple Select

Which numbers below are rational?

• $6.3589$
  

• $\sqrt{26}$

• $\sqrt{81}$

• $\frac{11}{2}$

• 7

Irrational Numbers

• Cannot be written in fraction form

• Decimals that are nonterminating or nonrepeating

• The square roots of non-perfect squares

Multiple Select

Which numbers below are irrational?

(dots in this case do not mean repeating)

•  $\pi$  

• 6 +  $\sqrt{30}$  

•  $0.123456.......$  

•  $\sqrt{32}$  

• - $\sqrt{121}$  

Multiple Choice

Ms. Finn wants to find the side length of a square that has an area of 150 feet. Should her answer be rational or irrational?

• Rational because $150\ \div\ 2$ is 75, and 75 can be written as a decimal

• Rational because 150 is a whole number so it can be written as a decimal.

• Irrational because $\sqrt{150}$ is not a perfect square

• Irrational because $150\ \div4$ is 37.5 which can't be written as a fraction.

Multiple Select

Which of the following is an example of an irrational number between 6 and 7?

• $2\pi$
  

• 6.875

• 6.12345....

Poll

How do you feel about identifying rational vs. irrational numbers?

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