Step 1:
The first step to converting 644.21728067416 to a fraction is to re-write 644.21728067416 in the form p/q where p and q are both positive integers. To start with, 644.21728067416 can be written as simply 644.21728067416/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 644.21728067416, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 644.21728067416/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 644.21728067416/1 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 644.21728067416 as a fraction:
14817/23 / 1