Write the repeating decimal as a fraction. .733733733 ______

Denote Decimal as x: Let's denote the repeating decimal 0.733733733... as x. x = 0.733733733... To isolate the repeating part, we multiply x by 1000 because there are three digits in the repeating sequence. 1000x = 733.733733... Now, we subtract the original x from 1000x to get rid of the decimal part. 1000x - x = 733.733733... - 0.733733733... This simplifies to: 999x = 733 Now, we divide both sides by 999 to solve for x. x = 733 / 999Multiply by 1000: We check if the fraction can be simplified. The numerator 733 and the denominator 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. $\newline$ $0.733733733$

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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

0.733733733

Denote Decimal as $x$ : Let's denote the repeating decimal $0.733733733\ldots$ as $x$ .
$x = 0.733733733\ldots$
To isolate the repeating part, we multiply $x$ by $1000$ because there are three digits in the repeating sequence.
$1000x = 733.733733\ldots$
Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part.
$1000x - x = 733.733733\ldots - 0.733733733\ldots$
This simplifies to:
$0.733733733\ldots$ $0$
Now, we divide both sides by $0.733733733\ldots$ $1$ to solve for $x$ .
$0.733733733\ldots$ $3$
Multiply by $1000$ : We check if the fraction can be simplified. The numerator $733$ and the denominator $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.