What is the one's digit when you multiply 100 nines together?

Answer 1

Consider the unit's digit when you multiply 9 n times.

n = 1 gives 9

n = 2 gives 1

n = 3 gives 9

n = 4 gives 1

and a pattern emerges. When n is even, as 100 is, the answer is 1.

Answer 2

You cannot do this on your calculator, because it doesn't have enough digits, but consider this:

9 x 9 x ....= 9100 = 9(2x50) = (92)50 = (81)50 = 81 x 81 x ....

Now, whenever you multiply 81 x 81, the ones digit will be 1 x 1 = 1, so the ones digit is 1.