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What is the least number of digits (including repetitions) needed to e

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What is the least number of digits (including repetitions) needed to e [#permalink]  02 Dec 2009, 07:19
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Question Stats:

73% (01:41) correct 27% (00:39) wrong based on 48 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
[Reveal] Spoiler: OA
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Re: What is the least number of digits (including repetitions) needed to e [#permalink]  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
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Re: What is the least number of digits (including repetitions) needed to e [#permalink]  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: What is the least number of digits (including repetitions) needed to e [#permalink]  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: What is the least number of digits (including repetitions) needed to e [#permalink]  03 Dec 2009, 04:26
Thanks guys. OA is indeed C.
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Re: What is the least number of digits (including repetitions) needed to e [#permalink]  26 Jan 2015, 16:07
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Re: What is the least number of digits (including repetitions) needed to e [#permalink]  26 Jan 2015, 21:10
Expert's post
wolver123 wrote:
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

I am guessing what put you off the question was "in decimal notation". It just means using the decimal system of counting (with 10 digits 0 - 9) as opposed to other systems such as binary (using only two digits 0 and 1) etc. Decimal notation is the usual system we use to write numbers. It has nothing to do with the decimal point.
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Re: What is the least number of digits (including repetitions) needed to e   [#permalink] 26 Jan 2015, 21:10
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