Write the repeating decimal as a fraction. .579579579 ______

Identify repeating decimal: Let's identify the repeating part of the decimal. The digits 579 are repeating.Represent as x: Let's represent the repeating decimal as x: x = 0.579579579...Shift decimal point: To convert the repeating decimal to a fraction, we multiply x by 1000 (since there are three digits in the repeating sequence) to shift the decimal point three places to the right: 1000x = 579.579579579...Subtract original x: Now, we subtract the original x from 1000x to get rid of the repeating decimals: 1000x - x = 579.579579579... - 0.579579579...Solve for x: This subtraction gives us: 999x = 579Find GCD: Now, we solve for x by dividing both sides of the equation by 999: x = 579 / 999Simplify fraction: We can simplify the fraction by finding the greatest common divisor (GCD) of 579 and 999. The GCD of 579 and 999 is 3.Final result: Divide both the numerator and the denominator by the GCD to simplify the fraction: x = (579 / 3) / (999 / 3)After simplification, we get: x = 193 / 333

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Write the repeating decimal as a fraction. $\newline$ $.579579579$

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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

.579579579

Identify repeating decimal: Let's identify the repeating part of the decimal. The digits $579$ are repeating.
Represent as $x$ : Let's represent the repeating decimal as $x$ : $x = 0.579579579\ldots$
Shift decimal point: To convert the repeating decimal to a fraction, we multiply $x$ by $1000$ (since there are three digits in the repeating sequence) to shift the decimal point three places to the right: $1000x = 579.579579579\ldots$
Subtract original x: Now, we subtract the original x from $1000x$ to get rid of the repeating decimals: $1000x - x = 579.579579579\ldots - 0.579579579\ldots$
Solve for x: This subtraction gives us: $999x = 579$
Find GCD: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{579}{999}$
Simplify fraction: We can simplify the fraction by finding the greatest common divisor (GCD) of $579$ and $999$ . The GCD of $579$ and $999$ is $3$ .
Final result: Divide both the numerator and the denominator by the GCD to simplify the fraction: $x = \frac{579 / 3}{999 / 3}$
Final result: Divide both the numerator and the denominator by the GCD to simplify the fraction: $x = \frac{579}{3} / \frac{999}{3}$ After simplification, we get: $x = \frac{193}{333}$