Write the repeating decimal as a fraction. .368368368 ______

Denote Decimal as x: Let's denote the repeating decimal 0.368368368... as x. x = 0.368368368... To isolate the repeating part, we multiply x by 1000 because the repeating part has three digits. 1000x = 368.368368368... Now, we subtract the original x from 1000x to get rid of the decimal part. 1000x - x = 368.368368368... - 0.368368368...Multiply by 1000: Perform the subtraction to isolate the non-repeating part. 1000x - x = 368 999x = 368 Now, we divide both sides by 999 to solve for x. x = 368/999Subtract to Eliminate Decimal: We should check if the fraction can be simplified. However, 368 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. $\newline$ $.368368368$

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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

.368368368

Denote Decimal as x: Let's denote the repeating decimal $0.368368368\ldots$ as $x$ .
$x = 0.368368368\ldots$
To isolate the repeating part, we multiply $x$ by $1000$ because the repeating part has three digits.
$1000x = 368.368368368\ldots$
Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part.
$1000x - x = 368.368368368\ldots - 0.368368368\ldots$
Multiply by $1000$ : Perform the subtraction to isolate the non-repeating part. $\newline$ $1000x - x = 368$ $\newline$ $999x = 368$ $\newline$ Now, we divide both sides by $999$ to solve for $x$ . $\newline$ $x = \frac{368}{999}$
Subtract to Eliminate Decimal: We should check if the fraction can be simplified. However, $368$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.