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Rational and Irrational Numbers Objective: I will identify rational and irrational numbers and identify repeating and terminating decimals MAFS.8.NS.1: Know that there are numbers that are not rational, and approximate them by rational numbers. MAFS.8.NS.1.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. (MP.2, MP.6, MP.7

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Do Now

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Rational and Irrational Numbers The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.

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You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3. 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. The same total area is shaded. 12 15 4 5 = 12 15 4 5

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Simplifying Fractions 16 80 16 = 1 4 4 80 = 5 4 4 ;16 is a common factor. 1515 = 16 80 Divide the numerator and denominator by 16. = 16 ÷ 16 80 ÷ 16 Simplify. = 0 for a ≠ 0 = 1 for a ≠ 0 = = – Remember! 0a0a a –7 8 7 –8 7878

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= –18 29 –18 29 18 = 2 9 29 = 1 29 ; there are no common factors. 18 and 29 are relatively prime. –18 29 Simplify. Simplifying Fractions

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= – 17 35 17 –35 17 = 1 17 35 = 5 7 ; there are no common factors. 17 and 35 are relatively prime. 17 –35 Check It Out: Example 1B Simplify.

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A repeating decimal can be written with a bar over the digits that repeat. So 1.3333… = 1.3. Writing Math _

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5.37 A. 5.37 7 is in the hundredths place. 37 100 = 5= 5 Writing Decimals as Fractions Write each decimal as a fraction in simplest form. 0.622 B. 0.622 2 is in the thousandths place. 622 1000 = = 311 500 Simplify by dividing by the common factor 2.

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Rational and Irrational Numbers Reflection: How do you change a repeating decimal into a fraction.

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