Graham's Number is a humongous beast, It is larger than we can express in exponential notation. It is larger than we can visualize. It is insanely larger than the largest number that any advanced technology that we can visualize, can visualize.
You don't believe me? Consider this :
A trillion is a very large number, but we can put it into context and visualize it ("a little less than the GDP of Australia in US dollars"). If you divide a trillion by 1000, you can immediately visualize the change - a mere billion ("what Bill Gates earned last year").
Graham's Number (GN) is so large, that there is no known method for differentiating GN and GN/1000. Or GN/(Googolplex), for that matter. That's right, a number so large that you can multiply or divide it by pretty much any number you can write in exponential notation, and the best mathematician in the world "observing" both numbers would not be able to say whether the new number was any different from GN.
I use the word "observing" in a theoretical sense, of course, as there is no known method of quantifying GN.