P.O.D. SolveP.O.D. Solve

6.6-Rational and 6.6-Rational and Irrational Irrational NumbersNumbersTo find and use To find and use decimal decimal representations representations of real #sof real #s

RATIONAL #S:RATIONAL #S: #s that can be #s that can be written as the written as the ratio of 2 ratio of 2 integers.integers.

*Note**Note*Rational #s can Rational #s can

also be decimals also be decimals that terminate that terminate

or repeat.or repeat.

IRRATIONAL #SIRRATIONAL #SAny real # that Any real # that is not rationalis not rational

Writing Writing Decimals as Decimals as Fractions:Fractions:Ex. 5.06Ex. 5.06

Answer: Answer:

Place the decimal portion over the

appropriate power of 10

The power of ten depends upon location

of last nonzero digit.

Example:Example:Write 0.1375 as a Write 0.1375 as a common fraction common fraction in lowest termsin lowest termsPlace 1375 over

104

How to convert a How to convert a repeatingrepeating

decimal into a decimal into a common fraction. common fraction.

..

2. Multiply both sides by 10n (where n is the # of digits in the block of repeating digits.)

1)Set equal X.

3. Subtract 1st equation from 2nd.

4. Then solve the resulting equation and reduce the resulting fraction.

You try:You try: