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