Convert the following repeating decimal to a fraction in simplest form.
., start overline, 2, 3, end overline
Let's represent the repeating decimal as x:
x = .23̅23̅
We know that this decimal repeats every two digits, so we can multiply it by 100 to shift the repeating part to the left:
100x = 23.23̅23̅
Now, we can subtract the original decimal from this shifted decimal:
100x - x = 23.23̅23̅ - .23̅23̅
Simplifying:
99x = 23
Dividing both sides by 99:
x = 23/99
Therefore, the repeating decimal .23̅23̅ can be written as the fraction 23/99 in simplest form.