Rational vs. Irrational Numbers

Check all that are true about rational numbers.

• They can be written as a fraction

• Their decimals terminate or repeat

• Their numbers are square roots of perfect squares

Check all that are true about irrational numbers.

• Cannot be written as a fraction

• Their decimals do not end and do not repeat

• Their numbers are square roots of non-perfect squares.

0.77777... is a rational number. Why?

-17 is a rational number. Why?

 $\sqrt{25}$  is a rational number, why?

0.15893... is an irrational number, explain why.

Is  $\sqrt{126}$  rational or irrational? Explain your reasoning.

Which of the following is an example of a rational number between 7 and 8?

• 7.83838383...

• 7.625

• 7 $\frac{1}{9}$

• Both a and c

• All of the above

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

• 2 $\pi$

• 6.875

• 6.12345...

• Both 2 $\pi$ and 6.12345...

• All of the above

Fill in the following statement with "either", "never", or "always" in order to make the statement true:

Square roots of perfect squares will _________________ be irrational numbers.