The Impossible Question

IMPOSSIBLE? HARDLY!.

9999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9980000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001=9.99999...... x 10^1,033 in Scientific Notation!!.

It's not "impossible," because the multiplication of any two real numbers is always defined......however, it DOES  result in a large answer....!!!!!!

That's like asking the square root of a million. No one will ever know.  (Nelson Muntz / The Simpsons).

Just kidding -- the Guest above beat me to it and gave the right answer. 

No kidding, that is the real answer.  Notice the one "8" in the group of "9's".

Turns out that when you multiply one group of nines by another group of nines, it follows a pattern.  All you have to do is count the 9's in each group.

Let i = the smaller number of nines, and let j = the larger number of nines.  Then the anwer will be as follows:

Write down (i - 1) "9's", followed by a single "8"

write down (j-i) "9's"

Write down (i - 1) "0's", followed by a single "1"

. . . and that's the answer!  Try it! 

For example, 3 "9's" multiplied by 7 "9's" [999 x 9999999 = ?].  In this case, i = 3 and j = 7.  The answer is (i - 1 = 2) "9's", followed by a single "8", followed by (j - i = 4) "9's", followed by (i - 1 = 2) "0's", followed by a single "1".  That is, the answer is 9989999001.

In your case, you had 427 "9's" (the 2nd group) multiplied by 650 "9's" (the 1st group).  It gives the answer above .  . . . exactly!

Kind of interesting really.  The kind of thing the "speed math" people love.  You can impress people by multiplying huge groups of "9's" in your head, just by following the simple rules above.  It's impressive when you rattle off the digits quickly and people don't realize the pattern.  

I'm sure that our venerable moderator could have given you the same answer -- he was just not in the mood to sort it out for us. 

By the way, I think the Guest above mis-typed.  In scientific notation the answer is approximately 9.999. . . x 10^1078

Oops!  I was too lazy to look at the Guest's answer carefully.

He has 516 "9's" followed by an "8", followed by 516 "0's", followed by a "1"  -- and that ain't right!

It SHOULD be 426 "9's", followed by an "8", followed by 223 "9's", followed by 426 "0's", followed by a "1".

It should be

99999999999999999999999999999999999999999999999999999999999999999999999999999999999

99999999999999999999999999999999999999999999999999999999999999999999999999999999999

99999999999999999999999999999999999999999999999999999999999999999999999999999999999

99999999999999999999999999999999999999999999999999999999999999999999999999999999999

99999999999999999999999999999999999999999999999999999999999999999999999999999999999

99999999999899999999999999999999999999999999999999999999999999999999999999999999999

99999999999999999999999999999999999999999999999999999999999999999999999999999999999

99999999999999999999999999999999999999999999999999999999999999999999900000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000

000000000000000000000000000000000000000000000000000000000000000000000000000000001

Also, I goofed on my scientific notation.   It should be approximately

9.999... * 10^1076