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Can the repeating decimal 0.272727... be expressed as a fraction? If so, complete the equation:

A) 99f = 1/2
B) 99f = 27/100
C) 99f = 1/9
D) 99f = 3/11

User Arben
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1 Answer

6 votes

Final answer:

The repeating decimal 0.272727... can be converted to a fraction and is equal to 3/11. The correct equation for this conversion is (D) 99f = 3/11.

Step-by-step explanation:

The repeating decimal 0.272727... can indeed be expressed as a fraction. To convert a repeating decimal to a fraction, you can set the decimal equal to a variable (let's call it f). In this case, f = 0.272727... Multiplying both sides by 100 to shift the decimal point two places gives 100f = 27.272727.... Then, subtract the original equation (f = 0.272727...) from this new equation to get 99f = 27, because 27.272727... minus 0.272727... is 27. Finally, to solve for f, divide both sides by 99 to get f = 27/99, which simplifies to f = 3/11. Therefore, the repeating decimal 0.272727... expressed as a fraction is 3/11, and the answer would be (D) 99f = 3/11.

User Brijesh Rakholia
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