Convert the following repeating decimal to a fraction in simplest form.
., start overline, 2, 3, end overline
.
23
To convert the repeating decimal .23¯ to a fraction, we can set it equal to a variable, x, and use algebra to solve for x.
x = .23¯
We multiply both sides of the equation by 100 to move the decimal point to the right, since there are two digits after the decimal point:
100x = 23.¯
Next, we subtract x from both sides of the equation to eliminate the repeating decimal:
100x - x = 23.¯ - .23¯
99x = 23
Now we solve for x by dividing both sides of the equation by 99:
x = 23/99
So the repeating decimal .23¯ can be written as the fraction 23/99, which is already in its simplest form.