a) Use a calculator to compute 2^161. Are you able to tell what the ones digit of this number is from the calculator’s display? Why or why not.
b) Determine the ones digit of 2^161. Explain your reasoning clearly.
2 answers
If your calculator won't compute that high a number... why not start with 2^2, then 2^3, then 2^4 and so on until you see the pattern : )
2^161 ≈ 3E48 ... 3 x 10^48
a) no ... not enough digits on calculator
b) 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , ...
the units digit repeats in a pattern of four numbers ... 2, 4, 8, 6
dividing 161 by 4 leaves a remainder of 1
... the 1st number in the repeating pattern is 2
... this is the units digit of 2^161
a) no ... not enough digits on calculator
b) 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , ...
the units digit repeats in a pattern of four numbers ... 2, 4, 8, 6
dividing 161 by 4 leaves a remainder of 1
... the 1st number in the repeating pattern is 2
... this is the units digit of 2^161
1 answer