Write the repeating decimal as a fraction. .556556556 ______

Assign Variable: Let's represent the repeating decimal 0.556556556... with a variable. Let x = 0.556556556...Multiply by 1000: To isolate the repeating part, we'll multiply x by 1000, since the repeating part has three digits. 1000x = 556.556556556...Subtract Original: Now, we subtract the original x from 1000x to get rid of the decimal part. 1000x - x = 556.556556556... - 0.556556556... This simplifies to: 999x = 556Divide by 999: To find the value of x, we divide both sides of the equation by 999. x = 556 / 999Simplify Fraction: We can simplify the fraction by looking for the greatest common divisor (GCD) of 556 and 999. The GCD of 556 and 999 is 1, so the fraction is already in its simplest form.Therefore, the repeating decimal 0.556556556... as a fraction is 556/999.

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Write the repeating decimal as a fraction. $\newline$ $.556556556$

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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

.556556556

Assign Variable: Let's represent the repeating decimal $0.556556556\ldots$ with a variable. $\newline$ Let $x = 0.556556556\ldots$
Multiply by $1000$ : To isolate the repeating part, we'll multiply $x$ by $1000$ , since the repeating part has three digits. $\newline$ $1000x = 556.556556556\ldots$
Subtract Original: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part. $\newline$ $1000x - x = 556.556556556... - 0.556556556...$ $\newline$ This simplifies to: $\newline$ $999x = 556$
Divide by $999$ : To find the value of $x$ , we divide both sides of the equation by $999$ . $x = \frac{556}{999}$
Simplify Fraction: We can simplify the fraction by looking for the greatest common divisor (GCD) of $556$ and $999$ . The GCD of $556$ and $999$ is $1$ , so the fraction is already in its simplest form.
Simplify Fraction: We can simplify the fraction by looking for the greatest common divisor (GCD) of $556$ and $999$ . The GCD of $556$ and $999$ is $1$ , so the fraction is already in its simplest form.Therefore, the repeating decimal $0.556556556\ldots$ as a fraction is $\frac{556}{999}$ .