Step 1:
The first step to converting 771.68749999945 to a fraction is to re-write 771.68749999945 in the form p/q where p and q are both positive integers. To start with, 771.68749999945 can be written as simply 771.68749999945/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 771.68749999945, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 771.68749999945/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 771.68749999945/1 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 771.68749999945 as a fraction:
12347/16 / 1