Rational - Irrational Numbers Review 1

Rational vs Irrational Numbers 1

Characteristics of Rational Numbers

• Can be expressed as a fraction

• Represent an exact amount

• Include terminating and repeating decimals

• Include roots of perfect squares and perfect cubes

Characteristics of Irrational numbers

• Cannot be expressed as a fraction

• Represents an approximation

• Decimal form is always non-repeating and non-terminating

• Includes roots of non-perfect square and cube roots

Multiple Choice

Which is an irrational number?

• a. 2.6

• $b.\ \sqrt{25}$

• $c.\ \sqrt{45}$

• $d.\ 3.\overline{25}$

Multiple Choice

Which is a rational number?

• $a.\ \sqrt{81}$

• $b.\ \sqrt{98}$

• c. 4.5486213...

• $d.\ \pi$

How do we know repeating decimals are rational?

• Because a repeating decimal can be converted to a fraction.

Multiple Choice

Convert 0.3444... to a fraction. Simplify if possible.

•  $a.\ \frac{34}{99}$  

•  $b.\ \frac{34}{90}$  

•  $c.\ \frac{31}{90}$  

•  $d.\ \frac{34}{9}$  

Multiple Choice

Solve

 $x^{3\ \ }=\ 64$  

• a. x = 8

• b. x = 4

• c. x = 16

• d. x = 262,144

Multiple Choice

Solve

 $x^2\ =\ 81$  

•  $a.\ x\ =\ \pm9$  

• b. x = 162

• c. x = 40.5

• d. x = 6,561

Multiple Choice

Which statement BEST describes

 $\sqrt{119}$  

• a. Between 10 and 11

• b. Between 11 and 12

• c. Between 12 and 13

• d. Between 9 and 10

Multiple Choice

Where does this irrational number fall on the number line?  $\sqrt{62}$  

• a. Between 6 and 7

• b. Between 7 and 8

• c. Between 8 and 9

• d. Between 9 and 10