Notes: Rational vs. Irrational
Question:
“Can all numbers be written as a fraction?”
______ Explain.
Examples: 0. 2 7.16 84
5 *This is a fraction already! 19.275
The Real Number System – includes Rational and Irrational numbers. (This is all the
numbers we’ve worked with so far – except “imaginary” numbers, like √−4 .)
It’s important that you can identify numbers as either Rational or Irrational.
Rational – Numbers that can be written as a fraction. These include: Integers, Whole
numbers, & Natural or Counting Numbers – basically all numbers except the “weird
ones”!!!
How do I read the diagram below???
Ex. Find 0.75. It is a Rational number and a REAL number
Ex. Find 0. It is an Integer, but it is also a Rational number and a REAL number.
Ex. Find 349. It is a Natural number, but it is also an Integer and Rational and a REAL number.
Ex. Find -2√5. It is just an Irrational number and a REAL number.
*Note: All numbers (Rational and Irrational) are REAL numbers except…______________________.
Irrational – Numbers that
cannot
be written as a fraction, AKA. the “weird” ones!
Let’s investigate…
What do you notice
about all of the numbers
in the Irrational circle?
Where do you think
“Imaginary” numbers go?
