Question

what fraction is equivalent to 0.55555555

Answer 1

The decimal 0.55555555... (where the 5 repeats indefinitely) can be expressed as a fraction.

Let \( x = 0.55555555... \).

To eliminate the repeating part, we can multiply both sides of the equation by 10:

\[
10x = 5.55555555...
\]

Now, we can subtract the original equation from this new equation:

\[
10x - x = 5.55555555... - 0.55555555...
\]

This simplifies to:

\[
9x = 5
\]

Now, divide both sides by 9:

\[
x = \frac{5}{9}
\]

So, the fraction equivalent to 0.55555555... is \(\frac{5}{9}\).