Write the repeating decimal as a fraction. .171171171 ______

Identify repeating pattern: Let's identify the repeating pattern in the decimal. The digits ＂171＂ repeat indefinitely.Represent as x: Let's represent the repeating decimal as x: x = 0.171171171...Multiply by 1000: To convert this repeating decimal into a fraction, we can multiply x by 1000, since the repeating pattern has three digits. This will shift the decimal point three places to the right: 1000x = 171.171171171...Subtract original x: Now, we subtract the original x from 1000x to get rid of the repeating decimals: 1000x - x = 171.171171171... - 0.171171171...Perform subtraction: Performing the subtraction, we get: 999x = 171Solve for x: Now, we solve for x by dividing both sides of the equation by 999: x = 171 / 999Find GCD: We can simplify the fraction by finding the greatest common divisor (GCD) of 171 and 999. The GCD of 171 and 999 is 9.Divide by GCD: Divide both the numerator and the denominator by the GCD to simplify the fraction: x = (171 / 9) / (999 / 9)Simplify fraction: After simplification, we get: x = 19 / 111

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Write the repeating decimal as a fraction. $\newline$ $.171171171$

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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

.171171171

Identify repeating pattern: Let's identify the repeating pattern in the decimal. The digits $171$ repeat indefinitely.
Represent as $x$ : Let's represent the repeating decimal as $x$ : $x = 0.171171171\ldots$
Multiply by $1000$ : To convert this repeating decimal into a fraction, we can multiply $x$ by $1000$ , since the repeating pattern has three digits. This will shift the decimal point three places to the right: $1000x = 171.171171171\ldots$
Subtract original x: Now, we subtract the original x from $1000x$ to get rid of the repeating decimals: $1000x - x = 171.171171171\ldots - 0.171171171\ldots$
Perform subtraction: Performing the subtraction, we get: $999x = 171$
Solve for x: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{171}{999}$
Find GCD: We can simplify the fraction by finding the greatest common divisor (GCD) of $171$ and $999$ . The GCD of $171$ and $999$ is $9$ .
Divide by GCD: Divide both the numerator and the denominator by the GCD to simplify the fraction: $x = \frac{171 / 9}{999 / 9}$
Simplify fraction: After simplification, we get: $x = \frac{19}{111}$