Real numbers

Real numbers

Learning objectives

Today I will learn:

• about the real number system

• about the difference between rational and irrational numbers

Bar Notation

• 0.5656565656565656565656...

•  $\frac{1}{3}$  

•  $0.\overline{3}$  or  $0.\overline{33}$  

Bar Notation

•  $x=0.\overline{56}$ 

•  $100x=56.\overline{56}$ 

•  $100x-x=56.\overline{56}-0.\overline{56}$  

•  $99x=56$  

•  $x=\frac{56}{99}$ 

Multiple Choice

Which one is greater?

• 0.3

• $0.\overline{3}$

Real Number system

Natural numbers

•  $N$  

• counting numbers

• 1, 2, 3, 4, 5, 6, ...

• 100,000,000

• 100,000,000,000

Whole numbers

•  $W$  

• natural numbers and 0

• 0, 1, 2, 3, 4, 5, ...

Integers

•   $Z$  

• whole valued positive or negative number or zero.

• ..., -3, -2, -1, 0, 1, 2, 3, ...

Rational numbers

•  $Q$  

•  $\frac{a}{b}$ 

• a & b = integers

•  $b\ne0$  

Who am I?

Rational and Irrational Numbers

Rational Numbers

 $\frac{a}{b}$  

a and b are integers 
 $b\ne0$  

Open Ended

Is 5 a rational number? Explain your answer.

Irrational Numbers

- cannot be written as $\frac{a}{b}$  

- decimals never repeat
- decimals never end

Multiple Choice

A repeating decimal is what type of number?

• Rational

• Irrational

Multiple Choice

A never ending and never repeating decimal is which type of number?

• Rational

• Irrational

Multiple Choice

0.25

• Rational

• Irrational

Multiple Choice

 $\pi$  

• Rational

• Irrational

Multiple Choice

 $0.\overline{21}$  

• Rational

• Irrational

What did you learn?