Write the repeating decimal as a fraction. .855855855 ______

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Identify Repeating Sequence: Identify the repeating sequence in the decimal. The repeating sequence in the decimal 0.855855855 is 855. This sequence repeats indefinitely, so we can denote the repeating decimal as 0.\overline{855}.Assign Variable: Let x equal the repeating decimal. Let x = 0.\overline{855}.Multiply by Power of 10: Multiply x by a power of 10 that will move the decimal point to the right so that the repeating sequence aligns with the original decimal. Since the repeating sequence is three digits long, we multiply x by 10^3 (which is 1000) to move the decimal point three places to the right. 1000x = 855.\overline{855}.Set Up Equation: Set up an equation to eliminate the repeating part. We now have two expressions: x = 0.\overline{855} and 1000x = 855.\overline{855}. By subtracting the first equation from the second, we can eliminate the repeating part. 1000x - x = 855.\overline{855} - 0.\overline{855}.Perform Subtraction: Perform the subtraction to solve for x. 1000x - x = 855.\overline{855} - 0.\overline{855} simplifies to 999x = 855.Divide by 999: Divide both sides of the equation by 999 to solve for x. x = 855 / 999.Simplify Fraction: Simplify the fraction. To simplify the fraction 855/999, we need to find the greatest common divisor (GCD) of 855 and 999. The GCD of 855 and 999 is 9.Divide both the numerator and the denominator by the GCD to get the simplified fraction. 855 ÷ 9 = 95 and 999 ÷ 9 = 111, so x = 95/111.

Write the repeating decimal as a fraction. $\newline$ $.855855855$

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Write the repeating decimal as a fraction.\newline.855855855.855855855.855855855

Write the repeating decimal as a fraction. $\newline$ $.855855855$