Step 1:
The first step to converting 513.14126374689 to a fraction is to re-write 513.14126374689 in the form p/q where p and q are both positive integers. To start with, 513.14126374689 can be written as simply 513.14126374689/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 513.14126374689, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 513.14126374689/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 513.14126374689/1 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 513.14126374689 as a fraction:
43617/85 / 1