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Re: Least number of digits

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Intern
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Re: Least number of digits [#permalink] New post 02 Dec 2009, 07:19
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A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 2 sessions
What is the least number of digits (including repetitions) needed to express 10^100 in decimal notation?

a) 4
b) 100
c) 101
d) 1000
e) 1001

Explanations please. Thanks
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Re: Least number of digits [#permalink] New post 02 Dec 2009, 08:02
10^n is a decimal number with a 1 followed by n zeros.
So 10^100 will include 100 0's + 1 digit for 1 = 101
So the answer is C.
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Re: Least number of digits [#permalink] New post 02 Dec 2009, 12:59
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This can easily be solved by looking at patterns of 10:

10^1=2 digits
10^2=3 digits
10^3=4 digits
10^4=5 digits
...so...
10^n=n+1 digits

thus:
10^{100}=101 digits
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Re: Least number of digits [#permalink] New post 02 Dec 2009, 13:32
10^2 is 1 followed by 2 zeroes in decimal notation

10^3 is 1 followed by 3 zeroes in decimal notation

10^4 is 1 followed by 4 zeroes in decimal notation

Hence 10^100 is 1 followed by 100 zeroes in decimal notation

Number of digits is 1 + 100 zeroes and hence answer C.
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Re: Least number of digits [#permalink] New post 03 Dec 2009, 04:26
Thanks guys. OA is indeed C.
Re: Least number of digits   [#permalink] 03 Dec 2009, 04:26
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Re: Least number of digits

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