5th grade math

[elmer]

please help! I am not familiar with unit digits.

2[n] means that 2 is used as a factor n times. For example, 2[4] means 2 x2 x2 x2 = 16. We say that 2[4] has a units digit of 6. If 2[1997] is multiplied out, what is the units (ones) digit of the product?

Is this a trick question? Do they mean what is 2[1] , which is 2 ???? :?

 

[Deleted member 4993]

please help! I am not familiar with unit digits.

2[n] means that 2 is used as a factor n times. For example, 2[4] means 2 x2 x2 x2 = 16. We say that 2[4] has a units digit of 6. If 2[1997] is multiplied out, what is the units (ones) digit of the product?

Is this a trick question? Do they mean what is 2[1] , which is 2 ???? :?

It is not a trick question.

\(\displaystyle 2^1 \ = \ 2 \\)? unit digit 2

\(\displaystyle 2^2 \ = \ 4 \\)? unit digit 4

\(\displaystyle 2^3 \ = \ 8 \\)? unit digit 8

\(\displaystyle 2^4 \ = \ 16 \\)? unit digit 6

\(\displaystyle 2^5 \ = \ 32 \\)? unit digit 2

\(\displaystyle 2^6 \ = \ 64 \\)? unit digit 4

\(\displaystyle 2^7 \ = \ 128 \\)? unit digit 8

\(\displaystyle 2^8 \ = \ 256 \\)? unit digit 6
.
.
.
\(\displaystyle 2^{4n+1} \ = \\)? unit digit 2

\(\displaystyle 2^{4n+2} \ = \\)? unit digit 4

\(\displaystyle 2^{4n+3} \ = \\)? unit digit 8

\(\displaystyle 2^{4n+4} \ = \\)? unit digit 6

where

n = 0, 1, 2, 3, 4, 5........

Does that help?