600-700 digits problem

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600-700 digits problem [#permalink]

22 Oct 2010, 12:42

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I had trouble interpreting and then solving this problem. Please advise

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

Last edited by shrouded1 on 22 Oct 2010, 15:51, edited 1 time in total.

corrected the question

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Re: 600-700 digits problem [#permalink]

22 Oct 2010, 15:52

rtaha2412 wrote:

I have corrected the question. It should say 10^{100}

This number is 1 followed by 100 zeroes, so you have 101 digits in all, hence the answer (c)
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Re: 600-700 digits problem [#permalink]

23 Oct 2010, 09:03

Consider 10^n, n being 1, 2, 3 ........

10^2 = 100 => 3 digits
10^3 = 1000 => 4 digits .... so on

number of digits for 10^n = n+1

10^100=> number of digits = 100+1 = 101

Correct option C

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Re: 600-700 digits problem [#permalink]

23 Oct 2010, 18:49

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Answer: C
Explanation:
The number of digits (least) for 10^n = (n+1) Where, n \geq 0.

So, The number of digits (least) for 10^{100} are 100 + 1 = 101
Thus the answer is C.

Or, you can see that there are one hundred 0's followed by 1 (to the right of 1) and the least number of digits would be number of 0's plus 1
==> 100+1=101
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Re: 600-700 digits problem [#permalink]

23 Oct 2010, 21:45

shrouded1 wrote:

rtaha2412 wrote:

I have corrected the question. It should say 10^{100}

This number is 1 followed by 100 zeroes, so you have 101 digits in all, hence the answer (c)

what is the meaning of decimal notation in this question and where did we use it?

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Re: 600-700 digits problem [#permalink]

25 Oct 2010, 00:24

C is the ans

10^2 = 100
10^3 =1 000
10^4 = 1 0000
so 10 ^100 willm be having 1 hunderd zeros = total digits = 1+ 100 = 101

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Re: 600-700 digits problem [#permalink]

25 Oct 2010, 19:45

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Hi utin,
Decimal notation is the writing of numbers in a base-10 numeral system. It derives its name from Deci = 10 I guess

examples = 55 = 10X5 + 5; 123 = (10^2)X1+(10^1)X2+(10^0)X3

This is the general numeric system used for expressing numbers.

Re: 600-700 digits problem [#permalink] 25 Oct 2010, 19:45

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600-700 digits problem

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600-700 digits problem

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