Write the repeating decimal as a fraction. .201201201 ______

Identify repeating decimal: Let's identify the repeating part of the decimal. The digits ＂201＂ repeat indefinitely.Convert decimal to fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as x: x = 0.201201201...Isolate repeating part: To isolate the repeating part, we can multiply x by 1000, since the repeating part is three digits long: 1000x = 201.201201201...Subtract original decimal: Now, subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 201.201201201... - 0.201201201...Perform subtraction: Perform the subtraction: 999x = 201Divide by 999: Now, divide both sides by 999 to solve for x: x = 201/999Find greatest common divisor: We can simplify the fraction by finding the greatest common divisor (GCD) of 201 and 999. The GCD of 201 and 999 is 3.Simplify the fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: x = (201/3) / (999/3) x = 67 / 333

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Write the repeating decimal as a fraction. $\newline$ $.201201201$

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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

.201201201

Identify repeating decimal: Let's identify the repeating part of the decimal. The digits $\text{＂}201\text{＂}$ repeat indefinitely.
Convert decimal to fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as $x$ : $x = 0.201201201\ldots$
Isolate repeating part: To isolate the repeating part, we can multiply $x$ by $1000$ , since the repeating part is three digits long: $1000x = 201.201201201\ldots$
Subtract original decimal: Now, subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 201.201201201\ldots - 0.201201201\ldots$
Perform subtraction: Perform the subtraction: $999x = 201$
Divide by $999$ : Now, divide both sides by $999$ to solve for $x$ : $x = \frac{201}{999}$
Find greatest common divisor: We can simplify the fraction by finding the greatest common divisor (GCD) of $201$ and $999$ . The GCD of $201$ and $999$ is $3$ .
Simplify the fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: $\newline$ $x = \frac{201/3}{999/3}$ $\newline$ $x = \frac{67}{333}$