Write the repeating decimal as a fraction. .683683683 ______

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits ＂683＂ repeat indefinitely.Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as x: x = 0.683683683...Isolate Repeating Part: To isolate the repeating part, we can multiply x by 1000, since the repeating part has three digits: 1000x = 683.683683683...Subtract Decimal: Now, we subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 683.683683683... - 0.683683683... 999x = 683Divide by 999: To find the value of x, we divide both sides of the equation by 999: x = 683 / 999Simplify Fraction: We can simplify the fraction by looking for common factors of the numerator and the denominator. Both 683 and 999 are divisible by 1, and there are no other common factors since 683 is a prime number.Final Fraction: Therefore, the fraction is already in its simplest form: x = 683 / 999

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Write the repeating decimal as a fraction. $\newline$ $.683683683$

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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

.683683683

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits $\text{“683”}$ repeat indefinitely.
Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as $x$ : $x = 0.683683683\ldots$
Isolate Repeating Part: To isolate the repeating part, we can multiply $x$ by $1000$ , since the repeating part has three digits: $1000x = 683.683683683\ldots$
Subtract Decimal: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part: $\newline$ $1000x - x = 683.683683683... - 0.683683683...$ $\newline$ $999x = 683$
Divide by $999$ : To find the value of $x$ , we divide both sides of the equation by $999$ : $x = \frac{683}{999}$
Simplify Fraction: We can simplify the fraction by looking for common factors of the numerator and the denominator. Both $683$ and $999$ are divisible by $1$ , and there are no other common factors since $683$ is a prime number.
Final Fraction: Therefore, the fraction is already in its simplest form: $x = \frac{683}{999}$