Write the repeating decimal as a fraction. .225225225 ______

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal 0.225225225... is 225.Assign Variable: Let x equal the repeating decimal. Let x = 0.225225225...Multiply by Power of 10: Multiply x by a power of 10 that moves the decimal point to the right so that the repeating pattern aligns with the original decimal. Since the repeating pattern is three digits long, we multiply x by 10^3 (which is 1000) to move the decimal point three places to the right. 1000x = 225.225225225...Subtract Equations: Subtract the original equation (x) from the new equation (1000x) to eliminate the repeating decimals. 1000x - x = 225.225225225... - 0.225225225... 999x = 225Solve for x: Solve for x by dividing both sides of the equation by 999. x = 225 / 999Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. The GCD of 225 and 999 is 9. x = (225 / 9) / (999 / 9) x = 25 / 111

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Write the repeating decimal as a fraction. $\newline$ $.225225225$

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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

.225225225

Identify Repeating Pattern: Identify the repeating pattern in the decimal. The repeating pattern in the decimal $0.225225225\ldots$ is $225$ .
Assign Variable: Let $x$ equal the repeating decimal. Let $x = 0.225225225\ldots$
Multiply by Power of $10$ : Multiply $x$ by a power of $10$ that moves the decimal point to the right so that the repeating pattern aligns with the original decimal. $\newline$ Since the repeating pattern is three digits long, we multiply $x$ by $10^3$ (which is $1000$ ) to move the decimal point three places to the right. $\newline$ $1000x = 225.225225225\ldots$
Subtract Equations: Subtract the original equation $x$ from the new equation $1000x$ to eliminate the repeating decimals. $\newline$ $1000x - x = 225.225225225... - 0.225225225...$ $\newline$ $999x = 225$
Solve for x: Solve for x by dividing both sides of the equation by $999$ . $\newline$ $x = \frac{225}{999}$
Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. $\newline$ The GCD of $225$ and $999$ is $9$ . $\newline$ $x = (\frac{225}{9}) / (\frac{999}{9})$ $\newline$ $x = \frac{25}{111}$