Write the repeating decimal as a fraction. .262262262 ______

Represent Decimal with Variable: Let's represent the repeating decimal 0.262262262... with a variable. Let x = 0.262262262...Multiply by 1000: To isolate the repeating part, we multiply x by 1000 because there are three digits in the repeating sequence. 1000x = 262.262262262...Subtract and Simplify: Now we subtract the original x from 1000x to get rid of the decimal part. 1000x - x = 262.262262262... - 0.262262262... This simplifies to: 999x = 262Divide by 999: To find the value of x, we divide both sides of the equation by 999. x = 262 / 999Check for Simplification: We can check if the fraction can be simplified by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than 1, so the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.262262262$

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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

.262262262

Represent Decimal with Variable: Let's represent the repeating decimal $0.262262262\ldots$ with a variable. $\newline$ Let $x = 0.262262262\ldots$
Multiply by $1000$ : To isolate the repeating part, we multiply $x$ by $1000$ because there are three digits in the repeating sequence. $\newline$ $1000x = 262.262262262\ldots$
Subtract and Simplify: Now we subtract the original $x$ from $1000x$ to get rid of the decimal part. $\newline$ $1000x - x = 262.262262262... - 0.262262262...$ $\newline$ This simplifies to: $\newline$ $999x = 262$
Divide by $999$ : To find the value of $x$ , we divide both sides of the equation by $999$ . $x = \frac{262}{999}$
Check for Simplification: We can check if the fraction can be simplified by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than $1$ , so the fraction is already in its simplest form.