Question

Write the following infinite decimal expression as a fraction you do not need to simplify
0.818818818…

Answer 1

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