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# 600-700 digits problem

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Intern
Joined: 19 Dec 2009
Posts: 33
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22 Oct 2010, 12:42
00:00

Difficulty:

35% (medium)

Question Stats:

57% (01:46) correct 43% (00:35) wrong based on 7 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

Last edited by shrouded1 on 22 Oct 2010, 15:51, edited 1 time in total.
corrected the question
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22 Oct 2010, 15:52
rtaha2412 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 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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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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23 Oct 2010, 18:49
1
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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 $$100 + 1 = 101$$

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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Joined: 27 Mar 2010
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23 Oct 2010, 21:45
shrouded1 wrote:
rtaha2412 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 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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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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25 Oct 2010, 19:45
1
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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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