Write the repeating decimal as a fraction. .800800800 ______

Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal 0.800800800... to a fraction.＂Identify Repeating Pattern: Identify the repeating pattern in the decimal. The pattern is ＂800＂ which repeats indefinitely.Define Variable: Let x be the repeating decimal, so x = 0.800800800...Shift Decimal Point: Multiply x by 1000 to shift the decimal point three places to the right, aligning the repeating digits. This gives us 1000x = 800.800800800...Subtract Decimals: Subtract the original x from 1000x to eliminate the repeating decimals. This gives us 1000x - x = 800.800800800... - 0.800800800...Simplify Equation: Perform the subtraction: 1000x - x = 800. This simplifies to 999x = 800.Divide to Solve: Divide both sides of the equation by 999 to solve for x. This gives us x = 800/999.Check for Simplification: Check if the fraction can be simplified. The numbers 800 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. $\newline$ $.800800800$

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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

.800800800

Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal $0.800800800\ldots$ to a fraction.＂
Identify Repeating Pattern: Identify the repeating pattern in the decimal. The pattern is $800$ which repeats indefinitely.
Define Variable: Let $x$ be the repeating decimal, so $x = 0.800800800\ldots$
Shift Decimal Point: Multiply $x$ by $1000$ to shift the decimal point three places to the right, aligning the repeating digits. This gives us $1000x = 800.800800800\ldots$
Subtract Decimals: Subtract the original $x$ from $1000x$ to eliminate the repeating decimals. This gives us $1000x - x = 800.800800800\ldots - 0.800800800\ldots$
Simplify Equation: Perform the subtraction: $1000x - x = 800$ . This simplifies to $999x = 800$ .
Divide to Solve: Divide both sides of the equation by $999$ to solve for $x$ . This gives us $x = \frac{800}{999}$ .
Check for Simplification: Check if the fraction can be simplified. The numbers $800$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.