Write the repeating decimal as a fraction. .716716716 ______

Identify Repeating Part: Let's identify the repeating part of the decimal. The digits 716 repeat indefinitely, so we can express the decimal as 0.716716716...Represent as x: Let's represent the repeating decimal as x: x = 0.716716716...Isolate Repeating Part: To isolate the repeating part, we can multiply x by 1000, since the repeating part is three digits long: 1000x = 716.716716716...Subtract Original x: Now, we subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 716.716716716... - 0.716716716...Perform Subtraction: Perform the subtraction: 999x = 716Solve for x: Now, we solve for x by dividing both sides of the equation by 999: x = 716/999Check Fraction Simplification: We can check if the fraction can be simplified. 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. $\newline$ $.716716716$

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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

.716716716

Identify Repeating Part: Let's identify the repeating part of the decimal. The digits $716$ repeat indefinitely, so we can express the decimal as $0.716716716\ldots$
Represent as $x$ : Let's represent the repeating decimal as $x$ : $x = 0.716716716\ldots$
Isolate Repeating Part: To isolate the repeating part, we can multiply $x$ by $1000$ , since the repeating part is three digits long: $1000x = 716.716716716\ldots$
Subtract Original $x$ : Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 716.716716716\ldots - 0.716716716\ldots$
Perform Subtraction: Perform the subtraction: $999x = 716$
Solve for x: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{716}{999}$
Check Fraction Simplification: We can check if the fraction can be simplified. The numerator and denominator do not have any common factors other than $1$ , so the fraction is already in its simplest form.