How can the repeating decimal 5.555… be expressed as a fraction?

To convert the repeating decimal 5.555… into a fraction, we can follow a few straightforward steps.

Let’s denote the repeating decimal as:

x = 5.555...

Now, observe that the decimal part .555… repeats indefinitely. To isolate the repeating part, we’ll multiply both sides of the equation by 10:

10x = 55.555...

Next, we can set up an equation using these two expressions for x:

10x - x = 55.555... - 5.555...

This simplifies to:

9x = 50

Now, solve for x:

x = \frac{50}{9}

Therefore, the repeating decimal 5.555… can be expressed as the fraction:

5.555... = \frac{50}{9}

In conclusion, 5.555… as a fraction is \frac{50}{9}.