1. Chapter 6 Irrational and Complex Numbers
Algebra 2
Chapter 6 Irrational and Complex Numbers

2. 6-6 Rational and Irrational Numbers
WARMUP
Write the following as fractions:
0.7
0.25
1.5
2.35
0.004

3. 6-6 Rational and Irrational Numbers
Goal:
To find and use decimal representations of real numbers…

4. 6-6 Rational and Irrational Numbers
Completeness Property of Real Numbers:
Every real number has a decimal representation, and every decimal represents a real number.

5. 6-6 Rational and Irrational Numbers
Recall that a rational number is any number that can be expressed as the ratio, or quotient, of two integers.
What is the easiest way to find the decimal representation of a rational number? (Without a calculator, of course.)

6. 6-6 Rational and Irrational Numbers
LONG DIVISION!!!

7. 6-6 Rational and Irrational Numbers
Find the following:

8. 6-6 Rational and Irrational Numbers
What were the results of the previous examples:

9. 6-6 Rational and Irrational Numbers
The decimal representation of any rational number is either terminating or repeating.
EVERY terminating or repeating decimal represents a rational number, meaning it can be written as a ratio:

10. 6-6 Rational and Irrational Numbers
So how do we find a fraction for a decimal?
What does equal as a fraction in lowest terms?

11. 6-6 Rational and Irrational Numbers
What about a repeating decimal? Express this repeating decimal as a common fraction in lowest terms:
Do on the board…

12. 6-6 Rational and Irrational Numbers
Remember that an irrational number is areal number that is not rational.
The decimal representation of any irrational number is infinite and nonrepeating.
Every infinite and nonrepeating decimal represents an irrational number.

13. 6-6 Rational and Irrational Numbers
Keep in mind that a calculator’s display will only give you a rational approximation of any irrational number.
My TI reports the  = We know that  is irrational and continues, non-repeating, infinitely.

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Homework

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