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Home Q & A Board Science-Related Homework Help Mathematics
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Smithpatrick Smithpatrick
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Posts: 35
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12 years ago
I already have found that it equals 5.15377521x10(to the power of 47) but my calculator wont multiply that!I need to know what the number in the ONES place is for the answer to 3 to the power of 100!Please help me im very confused!
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wrote...
#1
12 years ago
I got the same answer.5.153775208 x 10^47
wrote...
#2
12 years ago
5.15377521
5 Ones
wrote...
#3
12 years ago
cycle for power of 3 = {3 -> 9 -> 7 -> 1}

3^(4k+1) = 3 mod 10
3^(4k+2) = 9 mod 10
3^(4k+3) = 7 mod 10
3^(4k) = 1 mod 10

since 100 = 0 mod 4,
3^100 = (3^4)^25 = 1^25 mod 10 = 1 mod 10

answer = 1
wrote...
#4
12 years ago
We can see that 9^2=81
                        99^2=9801
                      999^2=998001
so,99...nth digit^2=(n-1)9 8(n-1)0 1
now 3^100=(3^2)50=9^50
                         =99...49th digit 8 000..49th digit 1
Ans:1 is in the ones place.
wrote...
#5
12 years ago
5.15378E+47


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