Write the repeating decimal as a fraction. .962962962 ______

Define x as decimal: Let x be the repeating decimal 0.962962962... We express this algebraically as: x = 0.962962962...Multiply by 1000: To isolate the repeating part, we multiply x by 1000, because there are three digits in the repeating sequence (962). 1000x = 962.962962...Subtract original equation: We subtract the original equation (x = 0.962962962...) from the new equation (1000x = 962.962962...) to get rid of the repeating decimals. 1000x - x = 962.962962... - 0.962962962...Perform subtraction: Perform the subtraction on both sides of the equation. 1000x - x = 962 999x = 962Solve for x: Solve for x by dividing both sides of the equation by 999. x = 962 / 999Simplify the fraction: Simplify the fraction if possible. In this case, 962 and 999 have no common factors other than 1, so the fraction is already in its simplest form. x = 962 / 999

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Write the repeating decimal as a fraction. $\newline$ $.962962962$

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Precalculus

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.962962962

Define $x$ as decimal: Let $x$ be the repeating decimal $0.962962962...$ $\newline$ We express this algebraically as: $\newline$ $x = 0.962962962...$
Multiply by $1000$ : To isolate the repeating part, we multiply $x$ by $1000$ , because there are three digits in the repeating sequence ( $962$ ). $\newline$ $1000x = 962.962962\ldots$
Subtract original equation: We subtract the original equation $x = 0.962962962\ldots$ from the new equation $1000x = 962.962962\ldots$ to get rid of the repeating decimals. $\newline$ $1000x - x = 962.962962\ldots - 0.962962962\ldots$
Perform subtraction: Perform the subtraction on both sides of the equation. $\newline$ $1000x - x = 962$ $\newline$ $999x = 962$
Solve for x: Solve for x by dividing both sides of the equation by $999$ . $\newline$ $x = \frac{962}{999}$
Simplify the fraction: Simplify the fraction if possible. In this case, $962$ and $999$ have no common factors other than $1$ , so the fraction is already in its simplest form. $\newline$ $x = \frac{962}{999}$