Step 1:
The first step to converting 1564.565 to a fraction is to re-write 1564.565 in the form p/q where p and q are both positive integers. To start with, 1564.565 can be written as simply 1564.565/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 1564.565, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 1564.565/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 1564.565/1 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 1564.565 as a fraction:
35985/23 / 1