Warmup

Is 3.121212…rational or irrational? (guess if you don’t know)

3.1: Rational and Irrational NumbersLEQ: What is the difference between rational and irrational numbers and how do you graph them on a number line?

A number line represents all real numbers. (not just integers)Ex.

Real numbers can be separated into either rationals or irrationals.

REAL NUMBERSRationals or Irrationals

A rational number is any number that can be expressed as a fraction.

An irrational number is any number with a nonrepeating and neverending decimal

Examples

Rational Irrational

You try: Sort the numbers into categories

-1, 3.5, -1.1111333242315…., π, -13, 20, 1.13131313…, 9.9834298023…,

Rational Irrational

Square root- the square root of a number is one of two identical factors of a number.

Ex) √16=___

Ex) √36=___

Ex) √81=___

What is √5?

(what does your calculator say?)

Rational or Irrational?

1) 4/7 2) √33) .33333…

4) -6 5) √6.25 6) π

Write down a number (rational or irrational)

Put the numbers in order from least to greatest. (hint: you can use a calculator to get the decimal representations)

-2/3, -√2, 1.444…, π, .25, 1/3, √10

Replace each ___ with <,>, or =.7.) -.75___3/4 8) 3/8___.374

9.) 5/3___1.666… 10) -10+6___4(2)(-3)