Question

Convert the following repeating decimal to a fraction in simplest form.
., start overline, 2, 3, end overline
.
23

Answer 1

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.