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

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Intern
Joined: 08 Aug 2009
Posts: 22
What is the least number of digits (including repetitions) needed to e [#permalink]

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02 Dec 2009, 08:19
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Difficulty:

25% (medium)

Question Stats:

68% (01:39) correct 32% (00:59) wrong based on 162 sessions

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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
Manager
Joined: 19 Nov 2007
Posts: 222
Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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02 Dec 2009, 09:02
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
Intern
Joined: 31 Oct 2009
Posts: 38
Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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02 Dec 2009, 13:59
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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:
$$10^{100}=101 digits$$
Intern
Joined: 11 Nov 2009
Posts: 10
Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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02 Dec 2009, 14:32
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.
Intern
Joined: 08 Aug 2009
Posts: 22
Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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03 Dec 2009, 05:26
Thanks guys. OA is indeed C.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15917
Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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26 Jan 2015, 17:07
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Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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26 Jan 2015, 22:10
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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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Posts: 15917
Re: What is the least number of digits (including repetitions) needed to e [#permalink]

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19 Apr 2016, 00:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Intern
Joined: 28 Sep 2016
Posts: 1
What is the least number of digits (including repetitions) needed to e [#permalink]

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28 Sep 2016, 11:07
10^(-1)×10^101= 10^100
Can also be written in decimal notation as 0.1×10^101 = 10^100
What is the least number of digits (including repetitions) needed to e   [#permalink] 28 Sep 2016, 11:07
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