Write the repeating decimal as a fraction. .893893893 ______

Identify repeating part: Let x equal the repeating decimal 0.893893893... x = 0.893893893... Identify the repeating part of the decimal. The repeating part is 893.Shift decimal point: Multiply x by 1000 to shift the decimal point three places to the right, since the repeating part has three digits. 1000x = 893.893893... Now we have the same repeating decimal part on both sides of the equation.Eliminate repeating part: Subtract the original equation (x = 0.893893893...) from the new equation (1000x = 893.893893...) to eliminate the repeating part. 1000x - x = 893.893893... - 0.893893893... This will give us an equation without the repeating decimal.Find value of 999x: Perform the subtraction to find the value of 999x. 999x = 893 Now we have an equation without the repeating decimal.Solve for x: Divide both sides of the equation by 999 to solve for x. x = 893 / 999 This gives us the fraction form of the repeating decimal.Simplify fraction: Simplify the fraction if possible. Both the numerator and the denominator have a common factor of 1, so the fraction is already in its simplest form. x = 893 / 999

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Write the repeating decimal as a fraction. $\newline$ $.893893893$

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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

.893893893

Identify repeating part: Let $x$ equal the repeating decimal $0.893893893\ldots$ $x = 0.893893893\ldots$ Identify the repeating part of the decimal.The repeating part is $893$ .
Shift decimal point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, since the repeating part has three digits. $\newline$ $1000x = 893.893893\ldots$ $\newline$ Now we have the same repeating decimal part on both sides of the equation.
Eliminate repeating part: Subtract the original equation $x = 0.893893893...$ from the new equation $1000x = 893.893893...$ to eliminate the repeating part. $\newline$ $1000x - x = 893.893893... - 0.893893893...$ $\newline$ This will give us an equation without the repeating decimal.
Find value of $999x$ : Perform the subtraction to find the value of $999x$ . $999x = 893$ Now we have an equation without the repeating decimal.
Solve for x: Divide both sides of the equation by $999$ to solve for $x$ . $\newline$ $x = \frac{893}{999}$ $\newline$ This gives us the fraction form of the repeating decimal.
Simplify fraction: Simplify the fraction if possible. $\newline$ Both the numerator and the denominator have a common factor of $1$ , so the fraction is already in its simplest form. $\newline$ $x = \frac{893}{999}$