Write the repeating decimal as a fraction. .044044044 ______

Identify repeating pattern: Question prompt: Write the repeating decimal 0.044044044... as a fraction.Assign variable x: Identify the repeating pattern in the decimal. The repeating pattern is 044.Shift decimal point: Let x equal the repeating decimal, so x = 0.044044044...Subtract original x: Multiply x by 1000 to shift the decimal point three places to the right, aligning the repeating digits. This gives us 1000x = 44.044044044...Perform subtraction: Subtract the original x from 1000x to eliminate the repeating decimals. This gives us 1000x - x = 44.044044044... - 0.044044044...Solve for x: Perform the subtraction: 1000x - x = 999x and 44.044044044... - 0.044044044... = 44. This results in the equation 999x = 44.Check fraction simplification: Solve for x by dividing both sides of the equation by 999. This gives us x = 44/999.Check if the fraction can be simplified. The numbers 44 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. $\newline$ $.044044044$

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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

.044044044

Identify repeating pattern: Question prompt: Write the repeating decimal $0.044044044\ldots$ as a fraction.
Assign variable $x$ : Identify the repeating pattern in the decimal. The repeating pattern is $044$ .
Shift decimal point: Let $x$ equal the repeating decimal, so $x = 0.044044044\ldots$
Subtract original x: Multiply $x$ by $1000$ to shift the decimal point three places to the right, aligning the repeating digits. This gives us $1000x = 44.044044044\ldots$
Perform subtraction: Subtract the original $x$ from $1000x$ to eliminate the repeating decimals. This gives us $1000x - x = 44.044044044... - 0.044044044...$
Solve for x: Perform the subtraction: $1000x - x = 999x$ and $44.044044044\ldots - 0.044044044\ldots = 44$ . This results in the equation $999x = 44$ .
Check fraction simplification: Solve for $x$ by dividing both sides of the equation by $999$ . This gives us $x = \frac{44}{999}$ .
Check fraction simplification: Solve for $x$ by dividing both sides of the equation by $999$ . This gives us $x = \frac{44}{999}$ .Check if the fraction can be simplified. The numbers $44$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.