Write the repeating decimal as a fraction. .020020020 ______

Identify repeating sequence: Identify the repeating sequence in the decimal. The repeating sequence in the decimal 0.020020020... is ＂020＂. This sequence repeats indefinitely.Let x equal: Let x equal the repeating decimal. Let x = 0.020020020...Multiply by power of 10: Multiply x by a power of 10 that will move the decimal point to the right so that the repeating sequence aligns with the original decimal. Since the repeating sequence is three digits long, we multiply x by 10^3 (which is 1000) to move the decimal point three places to the right. 1000x = 20.020020020...Subtract original from new: Subtract the original equation (x) from the new equation (1000x) to eliminate the repeating decimals. 1000x - x = 20.020020020... - 0.020020020... 999x = 20Solve for x: Solve for x by dividing both sides of the equation by 999. x = 20 / 999Simplify the fraction: Simplify the fraction if possible. The fraction 20/999 cannot be simplified further as 20 and 999 do not have any common factors other than 1.

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Write the repeating decimal as a fraction. $\newline$ $.020020020$

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Precalculus

Write a repeating decimal as a fraction

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Q. Write the repeating decimal as a fraction.

\newline

.020020020

Identify repeating sequence: Identify the repeating sequence in the decimal. The repeating sequence in the decimal $0.020020020\ldots$ is $\text{“020”}$ . This sequence repeats indefinitely.
Let $x$ equal: Let $x$ equal the repeating decimal. $\newline$ Let $x = 0.020020020\ldots$
Multiply by power of $10$ : Multiply $x$ by a power of $10$ that will move the decimal point to the right so that the repeating sequence aligns with the original decimal. $\newline$ Since the repeating sequence is three digits long, we multiply $x$ by $10^3$ (which is $1000$ ) to move the decimal point three places to the right. $\newline$ $1000x = 20.020020020\ldots$
Subtract original from new: Subtract the original equation $x$ from the new equation $1000x$ to eliminate the repeating decimals. $\newline$ $1000x - x = 20.020020020... - 0.020020020...$ $\newline$ $999x = 20$
Solve for x: Solve for x by dividing both sides of the equation by $999$ . $x = \frac{20}{999}$
Simplify the fraction: Simplify the fraction if possible. $\newline$ The fraction $\frac{20}{999}$ cannot be simplified further as $20$ and $999$ do not have any common factors other than $1$ .