Step 1:
The first step to converting 10566.628631421 to a fraction is to re-write 10566.628631421 in the form p/q where p and q are both positive integers. To start with, 10566.628631421 can be written as simply 10566.628631421/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 10566.628631421, which in this case is 9. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 10566.628631421/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 10566.628631421/1 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 10566.628631421 as a fraction:
84533/8 / 1