Rational vs Irrational

Convince Me!

100

Why is 0.75 rational?

Terminating Decimal

200

Why is -5 rational?

Integer

300

Why is 0.454545... rational?

Repeating Decimal

400

Why is √49 rational?

-Perfect Square

-7 is an Integer

500

Why is √2 irrational?

Non-Perfect Square

Decimal Detective

100

Is 0.125 rational or irrational? Explain.

Rational - Terminating

200

Is 0.333... rational or irrational?

Rational - Repeating Decimal

300

Is 0.58212121... rational or irrational?

Rational - Terminating

400

Is 0.7878878887... rational or irrational?

Irrational - Non-Repeating AND Non-Terminating

500

A number has a decimal that goes on forever. Can you determine that it is irrational on that informational alone?

No! You have to know whether it repeats or not.

Simplify It!

100

√25

5

200

5³

125

300

4²

16

400

∛216

6

500

√(100) + 1

11

Conversion Factory

100

Convert 25% to a decimal.

0.25

200

Convert 7/8 to a decimal.

0.875

300

Convert 0.67 to a percent.

67%

400

Convert 9% to a decimal.

0.09

500

Convert 0.45 to a fraction.

45/100

Identify and Justify

100

Is 3/4 rational or irrational? Explain.

Rational - Fraction

200

Is -9. rational or irrational? Explain.

Rational - Integer

300

Is √64 rational or irrational? Explain.

Rational - Perfect Square

400

Is √7 rational or irrational? Explain.

Rational - Non-Perfect Square

500

Is 8π rational or irrational?

Irrational - Non-Terminating AND Non-Repeating Decimal

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