Step 1:
The first step to converting 314.7698 to a fraction is to re-write 314.7698 in the form p/q where p and q are both positive integers. To start with, 314.7698 can be written as simply 314.7698/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 314.7698, which in this case is 4. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 314.7698/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 314.7698/1 each by 10000:
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 314.7698 as a fraction:
39661/126 / 1