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Exploring Repeated Decimals (LFP 5.3)Fractions with a numerator and a denominator that are integers can be expressed as a terminating or repeating decimal. It is also true that any terminating or repeating decimal can be expressed as a fraction with a numerator and denominator that are integers.Terminating decimals can be written as fractions with a power of 10—such as 10, 100, 1000, and 10,000—in the denominator. For example:0.75 can be expressed as 75100, or 341.414213562 can be expressed as 14142135621000000000In this problem, you will explore an interesting pattern that may give you some clues about how to write repeating decimals as fractions.Fill out the table, and write each fraction as a decimal:FractionDecimal1929394959697989Describe the pattern you see in your table.Use the pattern to write a decimal representation for each fraction. Use your calculator to check your answers.1. 992. 1093. 159What fraction is equivalent to each decimal? (Hint: the number 1.222… can be written as 1 + 0.222…)1. 1.2222….2. 2.7777….Explore decimal representations of fractions with a denominator of 99. Try 199, 299, 399, and so on. What patterns do you see?Explore decimal representations of fractions with a denominator of 99. Try 1999, 2999, 3999, and so on. What patterns do you see?Use the patterns you discovered in the decimal representations of fractions with denominators or 9, 99, and 999 to find fractions with these decimal representations.a. 0.3333…b. 0.0505050505….c. 0.45454545…d. 0.045045045045….e. 10.12121212…..f. 3.9999PRACTICE:Write a decimal representation of the fraction:1. 309 2. 52993. 1000999 ................
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