Write the repeating decimal as a fraction. .18181818 ______

Denote Decimal as x: Let's denote the repeating decimal 0.18181818... by x. x = 0.18181818... To convert this repeating decimal into a fraction, we can use algebra. We'll multiply x by a power of 10 that matches the length of the repeating pattern to shift the decimal point to the right so that the repeating digits align. Since the repeating pattern is two digits long (18), we'll multiply x by 100. 100x = 18.18181818...Multiply by 100: Now, we subtract the original x from 100x to get rid of the repeating decimal part. 100x - x = 18.18181818... - 0.18181818... This simplifies to: 99x = 18Subtract and Simplify: To find the value of x, we divide both sides of the equation by 99. x = 18 / 99Divide by 99: We can simplify the fraction by finding the greatest common divisor (GCD) of 18 and 99. The GCD of 18 and 99 is 9. x = (18/9) / (99/9) x = 2 / 11

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Write the repeating decimal as a fraction. $\newline$ $.18181818$

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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

.18181818

Denote Decimal as $x$ : Let's denote the repeating decimal $0.18181818\ldots$ by $x$ .
$x = 0.18181818\ldots$
To convert this repeating decimal into a fraction, we can use algebra. We'll multiply $x$ by a power of $10$ that matches the length of the repeating pattern to shift the decimal point to the right so that the repeating digits align.
Since the repeating pattern is two digits long ( $18$ ), we'll multiply $x$ by $100$ .
$100x = 18.18181818\ldots$
Multiply by $100$ : Now, we subtract the original $x$ from $100x$ to get rid of the repeating decimal part. $\newline$ $100x - x = 18.18181818... - 0.18181818...$ $\newline$ This simplifies to: $\newline$ $99x = 18$
Subtract and Simplify: To find the value of $x$ , we divide both sides of the equation by $99$ . $x = \frac{18}{99}$
Divide by $99$ : We can simplify the fraction by finding the greatest common divisor (GCD) of $18$ and $99$ . The GCD of $18$ and $99$ is $9$ . $\newline$ $x = \frac{18/9}{99/9}$ $\newline$ $x = \frac{2}{11}$