Write the repeating decimal as a fraction. .168168168 ______

Assign x value: Let x equal the repeating decimal 0.168168168... x = 0.168168168...Multiply by 1000: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating block has three digits (168). 1000x = 168.168168168...Subtract equations: Subtract the original equation (x = 0.168168168...) from the new equation (1000x = 168.168168168...) to eliminate the repeating decimals. 1000x - x = 168.168168168... - 0.168168168...Find value of 999x: Perform the subtraction to find the value of 999x. 999x = 168Divide by 999: Divide both sides of the equation by 999 to solve for x. x = 168 / 999Simplify fraction: Simplify the fraction by finding the greatest common divisor (GCD) of 168 and 999. The GCD of 168 and 999 is 3. x = (168 / 3) / (999 / 3)Divide both the numerator and the denominator by the GCD to get the simplified fraction. x = 56 / 333

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Write the repeating decimal as a fraction. $\newline$ $.168168168$

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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

.168168168

Assign $x$ value: Let $x$ equal the repeating decimal $0.168168168\ldots$ $\newline$ $x = 0.168168168\ldots$
Multiply by $1000$ : Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating block has three digits ( $168$ ). $\newline$ $1000x = 168.168168168\ldots$
Subtract equations: Subtract the original equation $x = 0.168168168...$ from the new equation $1000x = 168.168168168...$ to eliminate the repeating decimals. $\newline$ $1000x - x = 168.168168168... - 0.168168168...$
Find value of $999x$ : Perform the subtraction to find the value of $999x$ . $999x = 168$
Divide by $999$ : Divide both sides of the equation by $999$ to solve for $x$ . $x = \frac{168}{999}$
Simplify fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $168$ and $999$ . The GCD of $168$ and $999$ is $3$ . $\newline$ $x = \frac{168 / 3}{999 / 3}$
Simplify fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $168$ and $999$ . The GCD of $168$ and $999$ is $3$ .
$x = \frac{168}{3} / \frac{999}{3}$ Divide both the numerator and the denominator by the GCD to get the simplified fraction.
$x = \frac{56}{333}$