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....

Fill in the Blank

The square roots of perfect squares will (always, sometimes,never) be irrational numbers.

Fill in the Blank

Repeating decimals will (sometimes, always, never) be rational numbers

Fill in the Blank

Irrational Numbers will (always, sometimes, never) be able to be written as fractions

Poll

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

• Novice

• Apprentice

• Master

• Expert