Convert the following repeating decimal to a fraction in simplest form.
., start overline, 0, 6, end overline
Let's call the repeating decimal x.
We can start by multiplying both sides of the decimal by 100 to eliminate the decimal point:
100x = 6.06...
Next, we subtract the initial equation from this new equation to eliminate the repeating part:
100x - x = 6.06... - 0.06...
This simplifies to:
99x = 6
Now, we solve for x by dividing both sides of the equation by 99:
x = 6/99
Since the numerator and denominator share a common factor of 3, we can simplify the fraction further:
x = 2/33
Therefore, the repeating decimal 0.06... can be converted to the fraction 2/33 in simplest form.