What is the last digit in the expansion 3 to the 100th?

2 ⤊

What is the last digit in the expansion 3 to the 100th?

That is the question.

2006-12-11 10:05:33 · 5 answers · asked by Kyle C 2 in Science & Mathematics ➔ Mathematics

5 answers

zero

2006-12-11 10:07:41 · answer #1 · answered by Anonymous · 0⤊ 2⤋

2006-12-13 13:42:18 · answer #2 · answered by D.F 6 · 0⤊ 0⤋

Note the progression of the last digit in the powers of 3

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

3^5 = 243

The cycle begins again. So there is a cycle of four last digits. Every fourth digit is one.

So 3^100 = (3^4)^25 and ends in 1.

2006-12-11 10:22:52 · answer #3 · answered by Northstar 7 · 1⤊ 0⤋

(3^4)^25=last digit will be 1

2006-12-11 10:09:26 · answer #4 · answered by raj 7 · 1⤊ 0⤋

0 is the last digit.

2006-12-11 10:07:52 · answer #5 · answered by tacohombre13 1 · 0⤊ 2⤋