Write the repeating decimal as a fraction. .969969969 ______

Denote repeating decimal as x: Let's denote the repeating decimal 0.969696... as x. x = 0.969696... To convert this repeating decimal into a fraction, we will multiply x by a power of 10 that matches the length of the repeating pattern. Since the repeating pattern is two digits long (96), we will multiply x by 100. 100x = 96.969696...Multiply by power of 10: Now, we subtract the original x from 100x to get rid of the repeating decimal part. 100x - x = 96.969696... - 0.969696... 99x = 96Subtract original x from 100x: Next, we divide both sides of the equation by 99 to solve for x. x = 96 / 99Divide by 99: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. x = (96 / 3) / (99 / 3) x = 32 / 33

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Write the repeating decimal as a fraction. $\newline$ $.969969969$

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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

.969969969

Denote repeating decimal as $x$ : Let's denote the repeating decimal $0.969696...$ as $x$ .
$x = 0.969696...$
To convert this repeating decimal into a fraction, we will multiply $x$ by a power of $10$ that matches the length of the repeating pattern. Since the repeating pattern is two digits long ( $96$ ), we will multiply $x$ by $100$ .
$100x = 96.969696...$
Multiply by power of $10$ : Now, we subtract the original $x$ from $100x$ to get rid of the repeating decimal part. $\newline$ $100x - x = 96.969696... - 0.969696...$ $\newline$ $99x = 96$
Subtract original $x$ from $100x$ : Next, we divide both sides of the equation by $99$ to solve for $x$ . $x = \frac{96}{99}$
Divide by $99$ : We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $\newline$ $x = (\frac{96}{3}) / (\frac{99}{3})$ $\newline$ $x = \frac{32}{33}$