Step 1:
The first step to converting 1565.408298164 to a fraction is to re-write 1565.408298164 in the form p/q where p and q are both positive integers. To start with, 1565.408298164 can be written as simply 1565.408298164/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 1565.408298164, which in this case is 9. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 1565.408298164/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 1565.408298164/1 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 1565.408298164 as a fraction:
34439/22 / 1