Chapter 6 Irrational and Complex Numbers

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Presentation transcript:

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

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

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

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.

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 Rational and Irrational Numbers LONG DIVISION!!!

6-6 Rational and Irrational Numbers Find the following:

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

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:

6-6 Rational and Irrational Numbers So how do we find a fraction for a decimal? What does 0.0036 equal as a fraction in lowest terms?

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…

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.

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  = 3.141592654. We know that  is irrational and continues, non-repeating, infinitely.

6-6 Rational and Irrational Numbers Homework

6-6 Rational and Irrational Numbers

6-6 Rational and Irrational Numbers

6-6 Rational and Irrational Numbers