Problem Solving

What is the tenth digit to the right of the decimal point, in the decimal expansion of 1/(5^10) ?

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

ankur.agrawal wrote:What is the tenth digit to the right of the decimal point, in the decimal expansion of 1/(5^10) ?

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

1/(5^10) = 2^10/10^10 = 1024/10^10 = 0.0000001024

Answer C

stormier wrote:

ankur.agrawal wrote:What is the tenth digit to the right of the decimal point, in the decimal expansion of 1/(5^10) ?

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

1/(5^10) = 2^10/10^10 = 1024/10^10 = 0.0000001024

Answer C

Beautiful approach, stormier!

Let me modify your argument a little bit, just for the sake of "elegance"...

The tenth digit to the right of the decimal point of a certain number A = the units digit of (10^10) A, therefore:

10^10 A = (10^10)*[1/5^10] = 10^10 over 5^10 = (10/5)^10 = 2^10 = 1024 and we are done.

Regards,
Fabio.