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5-2 Rational Numbers

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Converting Decimals to Fractions To convert a decimal to a fraction: 1)Determine where the decimal ends 2)Place the numerals after the decimal over the appropriate denominator If there is a whole number, it stays whole, just add it on at the end. 3)Simplify Let’s try one….

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Converting Decimals to Fractions Convert 0.3 to a fraction using the steps in the previous slide. Step 1: determine where the decimal ends tenths tensonesDECIMAL POINT thousandths hundredths 03 Our decimal ends in the tenths place.

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Converting Decimals to Fractions Convert 0.3 to a fraction using the steps in the previous slide. Step 2: place the numerals after the decimal point over the appropriate denominator. Only 3 We discovered that our decimal ends in the tenths place. So our appropriate denominator is 10. 3 10

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Converting Decimals to Fractions Convert 0.3 to a fraction using the steps in the previous slide. Step 3: Simplify Can we simplify this fraction? No! is already in simplest form!

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Converting Decimals to Fractions Let’s try with 1.46. How do we convert it to a fraction? Step 1: determine where the decimal ends tenths tensonesDECIMAL POINT thousandths hundredths

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Converting Decimals to Fractions Let’s try with 1.46. How do we convert it to a fraction? Step 2: place the numerals after the decimal point over the appropriate denominator. We discovered that our decimal ends in the _________ place. So our appropriate denominator is _____.

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Converting Decimals to Fractions Let’s try with 1.46. How do we convert it to a fraction? Step 3: Simplify Can we simplify this fraction? 1 46 100

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Converting Decimals to Fractions When you have a repeating decimal, your appropriate denominator is a multiple of 9. 1)If the numerals after the decimal begin to repeat in the tenths place, our denominator is 9, if they begin to repeat in the hundredths place, our denominator is 99. Let’s try one….

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Converting Decimals to Fractions Convert 0.8 to a fraction. Step 1: determine where the decimal ends tenths tensonesDECIMAL POINT thousandths hundredths 08 Our decimal repeats after the tenths place. 88

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Converting Decimals to Fractions Convert 0.8 to a fraction. Step 2: place the numerals that repeat over the appropriate denominator. Only 8 We discovered that our decimal ends in the tenths place. So our appropriate denominator is 9. 8 9

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Converting Decimals to Fractions Convert 0.8 to a fraction. Step 3: Simplify Can we simplify this fraction? No! is already in simplest form! 8989 8989

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Converting Decimals to Fractions Let’s try with 0.64. Step 1: determine where the decimal repeats tenths tensonesDECIMAL POINT thousandths hundredths

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Converting Decimals to Fractions Let’s try with 0.64. Step 2: place the numerals that repeat over the appropriate denominator. We discovered that our decimal ends in the _________ place. So our appropriate denominator is _____.

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Converting Decimals to Fractions Let’s try with 0.64. Step 3: Simplify Can we simplify this fraction? 64 100

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The Number System

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Natural Numbers Natural numbers are all positive whole numbers that are not zero. These are also called counting numbers. 14 9 1,187 859 68

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Whole Numbers Whole numbers are all the natural numbers, plus zero. 14 9 1,187 859 68 0

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Integers Integers are all whole and natural numbers, plus the negatives. 14 9 1,187 859 68 -14 -9 -859 -68 -1,187 0

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Rational Numbers A rational number is any number that can be written as a simple fraction. This includes all the integers as well as fractions, terminating decimals, and repeating decimals, 1.1 ½ 0.333333… - 8

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Irrational Numbers A number that cannot be written as a simple fraction, or a number containing a decimal that goes on forever but does not repeat is called irrational. 0.02858294462… = 3.141592654

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HOW ABOUT A SONG? http://www.youtube.com/watch?v=m94WTZP14SA

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The Number System Natural Whole Rational Integers Irrational

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