Write the repeating decimal as a fraction. .313313313 ______

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits ＂313＂ repeat indefinitely.Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as x: x = 0.313313313...Isolate Repeating Pattern: To isolate the repeating pattern, we can multiply x by 1000, since the pattern repeats every three decimal places: 1000x = 313.313313313...Subtract and Simplify: Now, we subtract the original x from 1000x to get rid of the repeating decimals: 1000x - x = 313.313313313... - 0.313313313... 999x = 313Solve for x: Next, we solve for x by dividing both sides of the equation by 999: x = 313 / 999Simplify Fraction: We can simplify the fraction by looking for a common divisor. In this case, the numerator and denominator 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. $\newline$ $.313313313$

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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

.313313313

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits $\text{“313”}$ repeat indefinitely.
Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as $x$ : $x = 0.313313313...$
Isolate Repeating Pattern: To isolate the repeating pattern, we can multiply $x$ by $1000$ , since the pattern repeats every three decimal places: $1000x = 313.313313313\ldots$
Subtract and Simplify: Now, we subtract the original $x$ from $1000x$ to get rid of the repeating decimals: $1000x - x = 313.313313313... - 0.313313313...$ $999x = 313$
Solve for x: Next, we solve for x by dividing both sides of the equation by $999$ : $x = \frac{313}{999}$
Simplify Fraction: We can simplify the fraction by looking for a common divisor. In this case, the numerator and denominator do not have any common factors other than $1$ , so the fraction is already in its simplest form.