Write the repeating decimal as a fraction. .71717171 ______

Assign x value: Let x equal the repeating decimal 0.71717171... x = 0.71717171...Multiply by 100: Multiply both sides of the equation by 100 (since the repeating part is two digits long) to shift the decimal two places to the right. 100x = 71.71717171...Subtract equations: Subtract the original equation (x = 0.71717171...) from the new equation (100x = 71.71717171...) to eliminate the repeating decimals. 100x - x = 71.71717171... - 0.71717171...Find value of 99x: Perform the subtraction to find the value of 99x. 99x = 71Divide by 99: Divide both sides of the equation by 99 to solve for x. x = 71 / 99Check for simplification: Check if the fraction can be simplified. Since 71 and 99 have no common factors other than 1, the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.71717171$

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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

.71717171

Assign $x$ value: Let $x$ equal the repeating decimal $0.71717171\ldots$ $\newline$ $x = 0.71717171\ldots$
Multiply by $100$ : Multiply both sides of the equation by $100$ (since the repeating part is two digits long) to shift the decimal two places to the right. $\newline$ $100x = 71.71717171\ldots$
Subtract equations: Subtract the original equation $x = 0.71717171...$ from the new equation $100x = 71.71717171...$ to eliminate the repeating decimals. $\newline$ $100x - x = 71.71717171... - 0.71717171...$
Find value of $99x$ : Perform the subtraction to find the value of $99x$ . $99x = 71$
Divide by $99$ : Divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{71}{99}$
Check for simplification: Check if the fraction can be simplified. Since $71$ and $99$ have no common factors other than $1$ , the fraction is already in its simplest form.