Write the repeating decimal as a fraction. .440440440 ______

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal is ＂440＂.Assign Variable: Let x be the repeating decimal, so x = 0.440440440... Write this equation down to use it later.Shift Decimal Point: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating pattern has three digits. 1000x = 440.440440440...Subtract Decimals: Subtract the original x from 1000x to get rid of the repeating decimals. 1000x - x = 440.440440440... - 0.440440440... This results in 999x = 440.Solve for x: Solve for x by dividing both sides of the equation by 999. x = 440 / 999Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of 440 and 999. The GCD of 440 and 999 is 1, so the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.440440440$

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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

.440440440

Identify Repeating Pattern: Identify the repeating pattern in the decimal. $\newline$ The repeating pattern in the decimal is $＂440＂$ .
Assign Variable: Let $x$ be the repeating decimal, so $x = 0.440440440\ldots$ $\newline$ Write this equation down to use it later.
Shift Decimal Point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating pattern has three digits. $\newline$ $1000x = 440.440440440\ldots$
Subtract Decimals: Subtract the original $x$ from $1000x$ to get rid of the repeating decimals. $\newline$ $1000x - x = 440.440440440... - 0.440440440...$ $\newline$ This results in $999x = 440$ .
Solve for x: Solve for x by dividing both sides of the equation by $999$ . $\newline$ $x = \frac{440}{999}$
Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $440$ and $999$ . The GCD of $440$ and $999$ is $1$ , so the fraction is already in its simplest form.