Convert the following repeating decimal to a fraction in simplest form. .78 bar over 8
Let x = .78 bar over 8
To get rid of the repeating decimal, we multiply both sides of the equation by 100:
100x = 78.78 bar over 8
Next, we subtract the original equation from this new equation:
100x - x = 78.78 bar over 8 - .78 bar over 8
99x = 78
Dividing both sides of the equation by 99 gives us:
x = 78/99
This fraction can be simplified by finding the greatest common divisor (GCD) of 78 and 99, which is 3.
78/3 = 26 and 99/3 = 33
Therefore, .78 bar over 8 can be simplified to 26/33 in simplest form.