Convert 0.27(overlined) to a rational number in simplest form.
A. 27/100
B. 1/27
C. 3/11
D. 27/99
The overline indicates that the digit 27 repeats infinitely. To convert 0.27 overlined to a rational number, we can set x = 0.27 overlined, and then multiply both sides of the equation by 100 to eliminate the decimal:
100x = 27.27 overlined
Next, we subtract the left side of the equation from the right side:
100x - x = 27.27 overlined - 0.27 overlined
99x = 27.00 overlined
Now we need to eliminate the overline by multiplying both sides of the equation by 100:
9900x = 2700.00 overlined
Dividing both sides of the equation by 9900:
x = 2700.00 overlined / 9900 = 27/99
The simplest form of 27/99 is 3/11. Therefore, the answer is C. 3/11.