Convert the following repeating decimal to a fraction in simplest form .13 bar over 3
To convert the repeating decimal .13 bar over 3 to a fraction, we can set a variable x equal to the decimal and subtract it from a larger number.
Let x = .13 bar over 3
Multiplying both sides of the equation by 100 (to move the decimal place two places to the right) gives us:
100x = 13 bar over 3
Now, subtracting the original equation from the new equation:
100x - x = 13 bar over 3 - .13 bar over 3
99x = 13
Dividing both sides of the equation by 99:
x = 13/99
So, the repeating decimal .13 bar over 3 is equivalent to the fraction 13/99.