Step 1:
The first step to converting 5138.565 to a fraction is to re-write 5138.565 in the form p/q where p and q are both positive integers. To start with, 5138.565 can be written as simply 5138.565/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 5138.565, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 5138.565/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 5138.565/1 each by 1000:
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 5138.565 as a fraction:
82217/16 / 1