Write the following infinite decimal expression as a fraction you do not need to simplify

0.818818818…

1 answer

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 \( \frac{818}{999} \).