Write the repeating decimal as a fraction. .688688688 ______

Denote Decimal as x: Let's denote the repeating decimal 0.688688688... by the variable x. x = 0.688688688...Isolate Repeating Part: To convert the repeating decimal to a fraction, we first need to isolate the repeating part. We notice that the digits ＂688＂ are repeating. To isolate this repeating part, we multiply x by 1000 because there are three digits in the repeating sequence. 1000x = 688.688688688...Subtract and Solve: Now we subtract the original x from 1000x to get rid of the decimal part. This will give us an equation with x on both sides that we can solve for x. 1000x - x = 688.688688688... - 0.688688688... 999x = 688Divide and Simplify: Now we solve for x by dividing both sides of the equation by 999. x = 688 / 999Check Fraction: We should check if the fraction can be simplified. However, 688 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. $\newline$ $.688688688$

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Precalculus

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.688688688

Denote Decimal as $x$ : Let's denote the repeating decimal $0.688688688\ldots$ by the variable $x$ . $\newline$ $x = 0.688688688\ldots$
Isolate Repeating Part: To convert the repeating decimal to a fraction, we first need to isolate the repeating part. We notice that the digits ＂ $688$ ＂ are repeating. To isolate this repeating part, we multiply $x$ by $1000$ because there are three digits in the repeating sequence. $\newline$ $1000x = 688.688688688\ldots$
Subtract and Solve: Now we subtract the original $x$ from $1000x$ to get rid of the decimal part. This will give us an equation with $x$ on both sides that we can solve for $x$ . $\newline$ $1000x - x = 688.688688688... - 0.688688688...$ $\newline$ $999x = 688$
Divide and Simplify: Now we solve for $x$ by dividing both sides of the equation by $999$ . $x = \frac{688}{999}$
Check Fraction: We should check if the fraction can be simplified. However, $688$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.