Write the repeating decimal as a fraction. .61616161 ______

Denote decimal as x: Let's denote the repeating decimal 0.61616161... as x. x = 0.61616161... To isolate the repeating part, we multiply x by 100, since the repeating part is two digits long. 100x = 61.61616161... Now, we subtract the original x from 100x to get rid of the repeating decimal part. 100x - x = 61.61616161... - 0.61616161... 99x = 61 Now, we divide both sides by 99 to solve for x. x = 61/99Multiply by 100: We check if the fraction can be simplified. Both the numerator and the denominator have a common factor of 1, and there are no other common factors since 61 is a prime number. Therefore, the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.61616161$

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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

.61616161

Denote decimal as $x$ : Let's denote the repeating decimal $0.61616161...$ as $x$ .
$x = 0.61616161...$
To isolate the repeating part, we multiply $x$ by $100$ , since the repeating part is two digits long.
$100x = 61.61616161...$
Now, we subtract the original $x$ from $100x$ to get rid of the repeating decimal part.
$100x - x = 61.61616161... - 0.61616161...$
$0.61616161...$ $0$
Now, we divide both sides by $0.61616161...$ $1$ to solve for $x$ .
$0.61616161...$ $3$
Multiply by $100$ : We check if the fraction can be simplified. $\newline$ Both the numerator and the denominator have a common factor of $1$ , and there are no other common factors since $61$ is a prime number. $\newline$ Therefore, the fraction is already in its simplest form.