Write the repeating decimal as a fraction. .410410410 ______

Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal 0.410410410... to a fraction.＂Identify Repeating Part: Identify the repeating part of the decimal. The digits 410 repeat indefinitely, so we can express the decimal as 0.410410410...Assign Variable: Let x equal the repeating decimal: x = 0.410410410...Isolate Repeating Part: To isolate the repeating part, multiply x by 1000, because there are three digits in the repeating sequence: 1000x = 410.410410410...Subtract Decimals: Now subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 410.410410410... - 0.410410410...Solve for x: Perform the subtraction: 1000x - x = 999x and 410.410410410... - 0.410410410... = 410. This gives us the equation 999x = 410.Check for Simplification: Solve for x by dividing both sides of the equation by 999: x = 410/999.Check if the fraction can be simplified. The numbers 410 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. $\newline$ $.410410410$

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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

.410410410

Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal $0.410410410\ldots$ to a fraction.＂
Identify Repeating Part: Identify the repeating part of the decimal. The digits $410$ repeat indefinitely, so we can express the decimal as $0.410410410\ldots$
Assign Variable: Let $x$ equal the repeating decimal: $x = 0.410410410\ldots$
Isolate Repeating Part: To isolate the repeating part, multiply $x$ by $1000$ , because there are three digits in the repeating sequence: $1000x = 410.410410410\ldots$
Subtract Decimals: Now subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 410.410410410\ldots - 0.410410410\ldots$
Solve for x: Perform the subtraction: $1000x - x = 999x$ and $410.410410410... - 0.410410410... = 410$ . This gives us the equation $999x = 410$ .
Check for Simplification: Solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{410}{999}$ .
Check for Simplification: Solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{410}{999}$ .Check if the fraction can be simplified. The numbers $410$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.