Two large numbers of the fibonacci sequence are f51 = 20,365,011,074 and f52 = 32,951,280,099.what is the approximate value of the quotient ?

With the Fibonacci Sequence, we keep adding the 2 previous numbers
1
+1
=2

then
1
+2
=3

2 +
3
=5

And we can continue
8
13
21
34
55
89
144
233
377

If we take a Fibonacci number and divide it by the PREVIOUS Fibonacci number (For example 377 / 233) we get:
1.61802575107296

This is something known as the phi ratio, which equals (1 + sq root(5)) / 2
or 1.6180339887499
The further we carry out the Fibonacci sequence, the closer the division of (Fibonnaci Number "n") /(Fibonnaci Number "n-1") gets to be
(1 + sq root(5)) / 2
So, I would say that F52 / F51 would  equal 1.6180339887499 or be very close to it.
Look up the "Golden Ratio" in wkipedia

Rounded to the nearest tenth, it's 5.7
Hope this helps.