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**Convert Decimals to Fractions**

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Focus 4 - Learning Goal #1: Students will know that there are numbers that are not rational, and approximate them with rational numbers. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, students may: -Make connection with other concepts in math. - Make connection with other content areas. Students will know that there are numbers that are not rational, and approximate them with rational numbers. - Convert a decimal expansion that repeats into a fraction. - Approximate the square root of a number to the hundredth & explain the process. - For all items listed as a 2, students can explain their process. Students will know the subset of real numbers. - Know that all numbers have a decimal expansion. - Compare the size of irrational number. - Locate approximately irrational numbers on a number line. With help from the teacher, I have partial success with level 2 and 3. Even with help, students have no success with the unit content.

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Place Value Review Tens Ones . Tenths Hundredths Thousandths Ten Thousandths

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**What I already know… 0.5 = ½ 0.75 = ¾ 0.125 = 1/8**

0.5 = ½ = ¾ = 1/8 Use the place value of the last digit to determine the denominator. Drop the decimal and use that number as the numerator. In the decimal 0.5 the “5” is in the tenths place so the denominator will be “10.” The numerator will be 5. So the fraction is 5/10 which reduces to ½. In the decimal 0.75 the last digit is in the hundredths place so the denominator will be “100.” The numerator will be 75. So the fraction is 75/100 which reduces to ¾. In the decimal the last digit is in the thousandths place so the denominator will be “1000.” The numerator will be So the fraction is 125/1000 which reduces to 1/8.

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**Always REDUCE your fractions!**

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**Convert the following terminating decimals to fractions.**

0.4 4/10 Reduces to 2/5 1.86 1 and 86/100 Reduces to 1 43/50 0.795 795/1000 Reduces to 159/200

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**What about non-terminating decimals?**

How do you convert ….to a fraction? We are told that repeating decimals are rational numbers. However, to be a rational number it must be able to be written as a fraction of a/b.

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**Steps to change a non-terminating decimal to a fraction:**

Convert … to a fraction How many digits are repeating? 1 digit repeats Place the repeating digit over that many 9s. 1/9 Reduce, if possible. This means that the fraction 1/9 is equal to … With your calculator, divide 1 by 9. What do you get?

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**Try the steps again: Convert 0.135135135… to a fraction.**

How may digits are repeating? 3 digits repeat. Place the repeating digits over that many 9s. 135/999 Reduce if possible. This means that the fraction 135/999 which reduces to 5/37 is equal to … With your calculator, divide 135 by What do you get? Divide 5 by 37. What do you get?

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**One more time together:**

Convert … to a fraction. How many digits are repeating. 2 digits repeat. Place the repeating digits over that many 9s. 78/99 Reduce if possible. Divide the numerator and denominator by 3. This means that the fraction 4 78/99 reduces to /33 is equal to … With your calculator, divide 78 by What do you get? Divide 26 by 33. What do you get?

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**Your turn. Change the following repeating decimals to fractions.**

… 4/9 …. 154/99 = 1 54/99 … 36/99 = 4/11

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