Write the repeating decimal as a fraction. .825825825 ______

Identify repeating pattern: Identify the repeating pattern in the decimal. The digits 825 repeat indefinitely, so we can express the decimal as 0.825825825...Assign variable x: Let x equal the repeating decimal: x = 0.825825825...Multiply by 1000: Multiply x by 1000 (since there are three repeating digits) to shift the decimal point three places to the right: 1000x = 825.825825825...Subtract original equation: Subtract the original equation (x = 0.825825825...) from the new equation (1000x = 825.825825825...) to eliminate the repeating decimals: 1000x - x = 825.825825825... - 0.825825825...Perform subtraction: Perform the subtraction: 999x = 825Divide by 999: Divide both sides of the equation by 999 to solve for x: x = 825 / 999Find greatest common divisor: Simplify the fraction by finding the greatest common divisor (GCD) of 825 and 999. The GCD of 825 and 999 is 3.Simplify fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: x = (825 / 3) / (999 / 3)Calculate final fraction: Calculate the simplified fraction: x = 275 / 333

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Write the repeating decimal as a fraction. $\newline$ $.825825825$

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Algebra 2

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.825825825

Identify repeating pattern: Identify the repeating pattern in the decimal. The digits $825$ repeat indefinitely, so we can express the decimal as $0.825825825\ldots$
Assign variable x: Let $x$ equal the repeating decimal: $x = 0.825825825\ldots$
Multiply by $1000$ : Multiply $x$ by $1000$ (since there are three repeating digits) to shift the decimal point three places to the right: $1000x = 825.825825825\ldots$
Subtract original equation: Subtract the original equation $x = 0.825825825...$ from the new equation $1000x = 825.825825825...$ to eliminate the repeating decimals: $1000x - x = 825.825825825... - 0.825825825...$
Perform subtraction: Perform the subtraction: $999x = 825$
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ : $x = \frac{825}{999}$
Find greatest common divisor: Simplify the fraction by finding the greatest common divisor (GCD) of $825$ and $999$ . The GCD of $825$ and $999$ is $3$ .
Simplify fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: $x = \frac{825 / 3}{999 / 3}$
Calculate final fraction: Calculate the simplified fraction: $x = \frac{275}{333}$