Write the repeating decimal as a fraction. .788788788 ______

Denote Repeating Decimal: Let's denote the repeating decimal 0.788788788... as x. x = 0.788788788...Multiply and Isolate Repeating Part: To convert this repeating decimal into a fraction, we first need to isolate the repeating part. To do this, we can multiply x by 1000, since the repeating part is three digits long. 1000x = 788.788788788...Subtract and Simplify: Now, we subtract the original x from 1000x to get rid of the decimal part. 1000x - x = 788.788788788... - 0.788788788... This simplifies to: 999x = 788Divide to Find Value: To find the value of x, we divide both sides of the equation by 999. x = 788 / 999Check for Simplification: We can check if the fraction can be simplified by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than 1, so the fraction is already in its simplest form.

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Write the repeating decimal as a fraction. $\newline$ $.788788788$

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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

.788788788

Denote Repeating Decimal: Let's denote the repeating decimal $0.788788788\ldots$ as $x$ . $x = 0.788788788\ldots$
Multiply and Isolate Repeating Part: To convert this repeating decimal into a fraction, we first need to isolate the repeating part. To do this, we can multiply $x$ by $1000$ , since the repeating part is three digits long. $\newline$ $1000x = 788.788788788\ldots$
Subtract and Simplify: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part. $\newline$ $1000x - x = 788.788788788... - 0.788788788...$ $\newline$ This simplifies to: $\newline$ $999x = 788$
Divide to Find Value: To find the value of $x$ , we divide both sides of the equation by $999$ . $x = \frac{788}{999}$
Check for Simplification: We can check if the fraction can be simplified by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than $1$ , so the fraction is already in its simplest form.