To express the infinite decimal \( 0.818818818\ldots \) as a fraction, we can use the following method.
Let \( x = 0.818818818\ldots \). We notice that the repeating part is "818".
To eliminate the repeating part, we can multiply \( x \) by \( 1000 \) (since the repeating part has 3 digits):
\[ 1000x = 818.818818818\ldots \]
Now, we can set up the following equation by subtracting \( x \) from \( 1000x \):
\[ 1000x - x = 818.818818818\ldots - 0.818818818\ldots \]
This simplifies to:
\[ 999x = 818 \]
Now we can solve for \( x \):
\[ x = \frac{818}{999} \]
Thus, the decimal \( 0.818818818\ldots \) can be expressed as the fraction \( \frac{818}{999} \).
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