Step 1:
The first step to converting 309.65726104489 to a fraction is to re-write 309.65726104489 in the form p/q where p and q are both positive integers. To start with, 309.65726104489 can be written as simply 309.65726104489/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 309.65726104489, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 309.65726104489/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 309.65726104489/1 each by 100000000000:
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer for 309.65726104489 as a fraction:
10838/35 / 1