Write the repeating decimal as a fraction. .551551551 ______

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The repeating pattern is ＂551＂.Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as x: x = 0.551551551...Isolate Repeating Part: To isolate the repeating part, we multiply x by 1000 because there are three digits in the repeating pattern: 1000x = 551.551551...Subtract Decimal: Now, we subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 551.551551... - 0.551551551...Solve for x: Perform the subtraction: 999x = 551Simplify Fraction: Now, we solve for x by dividing both sides of the equation by 999: x = 551 / 999We can simplify the fraction by looking for the greatest common divisor (GCD) of 551 and 999. The GCD of 551 and 999 is 1, so the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $0.551551551$

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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

0.551551551

Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The repeating pattern is $＂551＂$ .
Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as $x$ : $x = 0.551551551\ldots$
Isolate Repeating Part: To isolate the repeating part, we multiply $x$ by $1000$ because there are three digits in the repeating pattern: $\newline$ $1000x = 551.551551\ldots$
Subtract Decimal: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part: $\newline$ $1000x - x = 551.551551... - 0.551551551...$
Solve for x: Perform the subtraction: $999x = 551$
Simplify Fraction: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{551}{999}$
Simplify Fraction: Now, we solve for $x$ by dividing both sides of the equation by $999$ : $x = \frac{551}{999}$ We can simplify the fraction by looking for the greatest common divisor (GCD) of $551$ and $999$ . The GCD of $551$ and $999$ is $1$ , so the fraction is already in its simplest form.