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Number properties

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Source: — Problem Solving |
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by stormier » Mon Feb 21, 2011 9:07 am
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
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by fskilnik@GMATH » Mon Feb 21, 2011 11:50 am
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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