largest number that can be formed using 3 nines?

Answer 1

A few notes to start off:
9^9=9^2•9^7=81•9^7 (not 81 as some people claim)

Therefore 9^(9^9) >>9^99=9^(9•11) =(9^9)^11>(9^9)^9>> 99^9

Thus the largest number using only 3 9s would be 9^(9^9) (this can be written without any mathematical symbols.

Someone suggested using Graham's notation (actually, it's Knuth's up-arrow notation).
if you were to allow one mathematical operator, then you could write 9↑(9^9)=9^(9^9)<<9^(9^9)!.

If you want to use two mathematical symbols, then you could switch to Conway chained arrow notation. Using a three chain, you could write
9→9→9=9↑↑↑↑↑↑↑↑↑9= 9↑↑↑↑↑↑↑↑(9↑↑↑↑↑↑↑↑9)

This is a number so large that if I made a tower of 9s (9^(9^(9^(9^(9 . . .))))), there is not enough space to write all of the 9s here. This number is absolutely huge, and you can keep adding !s to the end to increase it's size.

But there is something even more insane:

Steinhaus-Moser notation:
If you take the number 9^(9^9) and place it in a triangle, this number is represents (9^(9^9))^(9^(9^9)) Very large number, although not as large as 9→9→9, but only uses one mathematical symbol. . . and we can get even larger:

Take 9^(9^9) and place it in a square:
This represents 9^(9^9) in a triangle, that in a triangle, that in a triangle . . . until you have 9^(9^9) triangles. Ok, now we have an insanely large number, but we can always go larger.

The largest number (to my knowledge) written with only 3 9s and one mathematical symbol is 9^(9^9) in a circle. This is equivalent to 9^(9^9) nested in 9^(9^9) squares.

It has been proven that 10 in a circle is still smaller than Graham's number (the largest (known usuable) number), but I have a feeling that 9^(9^9) in a circle would be larger, not really sure though. But in any case, the largest number that you can have with 3 9's and n mathematical symbols (to the best of my knowledge) would be 9^(9^9) nested in n circles. The possibilities are endless.

Answer 2

9 to the power of 99

Answer 3

9 to the power of 9 to the power 9

Answer 4

"English Learner" and "Sara ireth" are completely wrong! 9^9 is NOT 81, it is 387420489 which is considerably higher. The largest value using only arithmetic signs and power is, as some have noted, 9^(9^9). Using only the four arithmetic operations, 9*9*9 (which is a mere 729) is the best you can do!

Answer 5

it's a 9*9*9=

Answer 6

actually there is a larger number than 9^99

this is written using a notation called Graham's Notation after the mathematician who devised it

Using Graham's notation we write
9^9 which is equivalent to 9 to the power 9
9^^9 is equivalent to 9 to the power (9 to the power 9)
9^^^9 is equivalent to 9 power (9 power (9 power 9) )

and so on

using Graham's Notation, the biggest number using just the digit 9 three times would therefore be

9^^^^^^^^^....^^^^^^^^^99 with as many ^s as you can write

which is basically infinite

Answer 7

9^9^9 = 9^81 < 9^99 < 99^9
the biggest nr is 99^9

9^99= 9^9 * 9^11
99^9= 9^9 * 11^9

and 9^11 > 11^9 cuz if we divide both nr with 9^9 in the left part there is 9^2 and int he right part there is (11/9)^9 = 1,(2)^9 which is way smaller than 9^2 :)

Answer 8

9^9^9

Answer 9

99928732364628361461741461617236812382535460624684..
and so on, there's no largest no, in this manner. If u wud have specified a bit more, than u could have been more near to the answer.

Answer 10

9^99 , and this is even larger than 9^(9^9), since 9^(9^9) is only 9^81. :)