Question

Convert the following repeating decimal to a fraction in simplest form.
., start overline, 0, 6, end overline

Answer 1

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.