To express 5 repeating (which can be written as 5.5555…) as a fraction, we can use a simple algebraic method.
Let’s denote the repeating decimal as x. So, we can write:
x = 5.5555…
Next, we want to eliminate the repeating part. We can do this by multiplying x by 10:
10x = 55.5555…
Now, if we subtract the first equation from this new equation, we get:
10x – x = 55.5555… – 5.5555…
This simplifies to:
9x = 50
Now, to solve for x, we divide both sides by 9:
x = 50/9
Thus, the decimal 5.5555… can be expressed as the fraction 50/9.
In summary, when we convert 5 repeating into a fraction, we find that it equals 50/9.