Step 1:
The first step to converting 689.77605468738 to a fraction is to re-write 689.77605468738 in the form p/q where p and q are both positive integers. To start with, 689.77605468738 can be written as simply 689.77605468738/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 689.77605468738, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 689.77605468738/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 689.77605468738/1 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 689.77605468738 as a fraction:
40007/58 / 1