Write the repeating decimal as a fraction. .388388388 ______

Identify Repeating Decimal: Let's identify the repeating part of the decimal. The digits ＂388＂ repeat indefinitely.Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as x: x = 0.388388388...Isolate Repeating Part: To isolate the repeating part, we multiply x by 1000 because there are three digits in the repeating sequence: 1000x = 388.388388388...Subtract Decimal: Now, we subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 388.388388388... - 0.388388388... This simplifies to: 999x = 388Divide by 999: To find the value of x, we divide both sides of the equation by 999: x = 388 / 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. $\newline$ $.388388388$

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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

.388388388

Identify Repeating Decimal: Let's identify the repeating part of the decimal. The digits $388$ repeat indefinitely.
Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as $x$ : $x = 0.388388388...$
Isolate Repeating Part: To isolate the repeating part, we multiply $x$ by $1000$ because there are three digits in the repeating sequence: $\newline$ $1000x = 388.388388388\ldots$
Subtract Decimal: Now, we subtract the original $x$ from $1000x$ to get rid of the decimal part: $\newline$ $1000x - x = 388.388388388... - 0.388388388...$ $\newline$ This simplifies to: $\newline$ $999x = 388$
Divide by $999$ : To find the value of $x$ , we divide both sides of the equation by $999$ : $x = \frac{388}{999}$
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.