Write the repeating decimal as a fraction. .366366366 ______

Identify Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal is ＂366＂.Assign Variable: Let x equal the repeating decimal, so x = 0.366366366... To convert this into a fraction, we need to isolate the repeating part.Shift Decimal Point: Multiply x by 1000 to shift the decimal point three places to the right, because there are three digits in the repeating pattern. 1000x = 366.366366366...Subtract Decimals: Subtract the original x from the 1000x to get rid of the repeating decimals. 1000x - x = 366.366366366... - 0.366366366... This gives us 999x = 366.Divide by 999: Divide both sides of the equation by 999 to solve for x. x = 366 / 999Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of 366 and 999. The GCD of 366 and 999 is 3.Simplify Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction. x = (366 / 3) / (999 / 3) x = 122 / 333

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Write the repeating decimal as a fraction. $\newline$ $.366366366$

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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

.366366366

Identify Pattern: Identify the repeating pattern in the decimal. $\newline$ The repeating pattern in the decimal is $＂366＂$ .
Assign Variable: Let $x$ equal the repeating decimal, so $x = 0.366366366\ldots$ $\newline$ To convert this into a fraction, we need to isolate the repeating part.
Shift Decimal Point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, because there are three digits in the repeating pattern. $\newline$ $1000x = 366.366366366\ldots$
Subtract Decimals: Subtract the original $x$ from the $1000x$ to get rid of the repeating decimals. $\newline$ $1000x - x = 366.366366366... - 0.366366366...$ $\newline$ This gives us $999x = 366$ .
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ . $x = \frac{366}{999}$
Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of $366$ and $999$ . The GCD of $366$ and $999$ is $3$ .
Simplify Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction. $\newline$ $x = \frac{366}{3} / \frac{999}{3}$ $\newline$ $x = \frac{122}{333}$