Write the repeating decimal as a fraction. .228228228 ______

Assign x value: Let x equal the repeating decimal 0.228228228... x = 0.228228228...Shift decimal point: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating block has three digits (228). 1000x = 228.228228228...Subtract to eliminate decimals: Subtract the original x from 1000x to eliminate the repeating decimals. 1000x - x = 228.228228228... - 0.228228228... 999x = 228Divide by 999: Divide both sides of the equation by 999 to solve for x. x = 228 / 999Simplify fraction: Simplify the fraction by finding the greatest common divisor (GCD) of 228 and 999. The GCD of 228 and 999 is 3. x = (228 / 3) / (999 / 3) x = 76 / 333

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Write the repeating decimal as a fraction. $\newline$ $.228228228$

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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

.228228228

Assign $x$ value: Let $x$ equal the repeating decimal $0.228228228\ldots$ $\newline$ $x = 0.228228228\ldots$
Shift decimal point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating block has three digits ( $228$ ). $\newline$ $1000x = 228.228228228\ldots$
Subtract to eliminate decimals: Subtract the original $x$ from $1000x$ to eliminate the repeating decimals. $\newline$ $1000x - x = 228.228228228... - 0.228228228...$ $\newline$ $999x = 228$
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ . $x = \frac{228}{999}$
Simplify fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $228$ and $999$ . The GCD of $228$ and $999$ is $3$ . $\newline$ $x = \frac{228 / 3}{999 / 3}$ $\newline$ $x = \frac{76}{333}$