Write the repeating decimal as a fraction. .119119119 ______

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits ＂119＂ repeat indefinitely.Express as x: Express the repeating decimal as x: x = 0.119119119...Multiply by 1000: To isolate the repeating pattern, multiply x by 1000 because there are three digits in the repeating pattern: 1000x = 119.119119119...Subtract Original x: Now subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 119.119119119... - 0.119119119...Perform Subtraction: Perform the subtraction: 999x = 119Divide by 999: Divide both sides by 999 to solve for x: x = 119/999Simplify Fraction: Simplify the fraction by looking for a common divisor. The numbers 119 and 999 do not have any 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. $\newline$ $.119119119$

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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

.119119119

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits $\text{＂}119\text{＂}$ repeat indefinitely.
Express as $x$ : Express the repeating decimal as $x$ : $x = 0.119119119\ldots$
Multiply by $1000$ : To isolate the repeating pattern, multiply $x$ by $1000$ because there are three digits in the repeating pattern: $1000x = 119.119119119\ldots$
Subtract Original $x$ : Now subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 119.119119119\ldots - 0.119119119\ldots$
Perform Subtraction: Perform the subtraction: $999x = 119$
Divide by $999$ : Divide both sides by $999$ to solve for $x$ : $x = \frac{119}{999}$
Simplify Fraction: Simplify the fraction by looking for a common divisor. The numbers $119$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.