Creating, Learning, and Laughing with Mrs. Kenney



Advanced MathConverting Repeating Decimals into FractionsName: Period:left1016000Guiding Questions: Are there decimals you cannot turn into fractions?How can you convert a terminating decimal into a fraction?How can you convert a repeating decimal into a fraction?-47528564306500 What are the three types of decimals we have discussed?Type of DecimalDefinitionExamplesTerminating DecimalA decimal where the digits behind the decimal STOP!0.89512.2Repeating DecimalA decimal where one or more digits behind the decimal infinitely reoccur.0.27272727…Non-terminating and Non-repeating decimalA decimal where the digits behind the decimal do not stop AND do not reoccur.3.616616661…12.8695326488… Which types of decimals can be converted into fractions?ONLY TERMINATING OR REPEATING DECIMALS CAN BE REWRITTEN AS FRACTIONS!-49876419017000Practice: Identify each of the following as terminating, repeating, or neither. Next, determine if you can write each decimal as a fraction. A. 1.646644666444… B.C.6.43434343…. D. 8.45667811247… E. F.2.9568-49873157423000How do you convert a terminating decimal into a fraction?Converting a terminating decimal into a fraction If there is a whole number, just re-write it.Determine the place value of the last digit behind your decimal point. Remember, all numbers to the right of the decimal point are fractions with denominators 10, 100, 1,000, 10,000, 100,000, etc.Write the place value of the last digit to the right of the decimal as the denominator of your fraction.Write all the digits to the right of the decimal point as the numerator of your fraction.Simplify if necessary.Practice: Convert each of the following decimals to fractions in simplest form. A. 4.375 B.9.8C.3.64-47643132378400What are some common repeating decimals that can be written as fractions?Practice: Convert each of the following decimals to fractions in simplest form. A. B.C.30939061642800How do you convert any repeating decimal into a fraction?Converting a repeating decimal into a fractionSet the repeating decimal equal to x.Examine the repeating decimal to determine how many digits are repeating in the repeating decimal.Place the repeating digit(s) to the left of the decimal point, by multiplying each side of your new equation by a power of 10 that has that many zeroes. For example: if you need to move your decimal two spaces to get the repeating decimal , multiply each side by 100 because 100 has two zeroes and there are two digits repeatingPlace the repeating digit(s) to the right of the decimal point using the same method.Subtract the two equations. Solve for x.Examples:Convert and into a fraction Example 1: StepsExample 2: Set the repeating decimal equal to x.Get the repeating decimal on the left of the decimalGet the repeating decimal on the right of the decimalGet the repeating decimal to the left and right of the decimal point.Get the repeating decimal on the left of the decimalRepeating decimal is already on the right of the decimalSubtract the two new equations. Be sure to line up your decimals!!!!!!!!!!!!!!!!Solve for xPractice: Convert each of the following decimals to fractions in simplest form. A. B.C. ................
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