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Lesson 7 Rational and Irrational Numbers

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Numbers Numbers can be classified as rational or irrational. What is the difference? Rational –Integers- all positive, whole numbers, their opposites and zero. –Ratio- Any number that can be written in a ratio of 2 integers. –Terminating decimals- decimals that end –Repeating decimals- they have a digit that goes on forever.

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Then what’s irrational? If a number can’t be written as the ratio of two integers, it is irrational. All non-terminating, non-repeating decimals are irrational. –3.14159265… we know this as pi. It is a non- repeating decimal. Its digits go on forever, but never repeat. –1.7320508…is irrational because when written as a decimal its digits never end and never repeat. There is no way to write non-terminating decimals as a ratio.

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Let’s Practice… Identify all of the irrational numbers in the list below: –3, ¼, 0, √8, √9 First we need to figure out what √8 and √9 are equal to. √8 is about 2.82842712, and √9 is 3. Which is irrational? Is the decimal for √2 a repeating or non- repeating decimal? –Find its value.

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How do we make a repeating decimal into a fraction? Usually when we change a decimal to a fraction, we put it over 10, 100 or 1,000..2= 2/10 or 1/5.57 = 57/100.649 = 649/1000 How would we put.8(repeating) into a fraction? –Since it is repeating, there is not definite place value, what do we put it over? –The fraction. 1/9 has a repeating decimal of.1(repeating), so, the fraction we would write would be 8/9.

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Practice time! What decimal represents √5? What is the decimal equivalent to 4/9? Which number is a rational number? 0.76, 0.83961257…, √10, √14 What decimal is equivalent to 2/3? An irrational number is….

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Last but not least Look at the list of numbers below. Π, -0.005, -9/7, √12, √81 –Name two different irrational numbers in the list above. –Explain how you know that each number you chose is irrational.

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