Step 1:
The first step to converting 684.21730301416 to a fraction is to re-write 684.21730301416 in the form p/q where p and q are both positive integers. To start with, 684.21730301416 can be written as simply 684.21730301416/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 684.21730301416, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 684.21730301416/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 684.21730301416/1 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 684.21730301416 as a fraction:
15737/23 / 1