Step 1:
The first step to converting 5638.589996629 to a fraction is to re-write 5638.589996629 in the form p/q where p and q are both positive integers. To start with, 5638.589996629 can be written as simply 5638.589996629/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 5638.589996629, which in this case is 9. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 5638.589996629/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 5638.589996629/1 each by 1000000000:
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 5638.589996629 as a fraction:
95856/17 / 1