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# What is the tenth digit to the right of the decimal point

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What is the tenth digit to the right of the decimal point  [#permalink]

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18 Feb 2011, 02:37
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21
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Difficulty:

75% (hard)

Question Stats:

51% (01:41) correct 49% (01:34) wrong based on 1070 sessions

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What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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18 Feb 2011, 03:41
12
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$$(\frac{1}{5})^{10}$$

$$\frac{1}{5^{10}}$$

$$\frac{1}{(\frac{10}{2})^{10}}$$

$$\frac{2^{10}}{{10}^{10}}$$

$$\frac{1024}{{10}^{10}}$$

$$1024*10^{-10}$$

$$.0000001024$$

Tenth digit to the right of decimal is 4.

Ans: "C"
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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18 Feb 2011, 04:38
(1/5)^10 is same as (2/10)^10. 10th digit after decimal in this is same as unit's digit in 2^10
2^10 = 2^5*2^5 - 32*32 whose units digit would be 4
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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30 Nov 2011, 03:09
2
Hi fluke,

but, inasmuch as I know tenth digit to the right of the decimal point is a first number after the decimal point. Please correct if I am wrong!
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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30 Nov 2011, 03:53
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1
feruz77 wrote:
Hi fluke,

but, inasmuch as I know tenth digit to the right of the decimal point is a first number after the decimal point. Please correct if I am wrong!

You are talking about the 'tenths' digit which is right after the decimal point.
'The tenth digit to the right of the decimal' is the digit that appears after 9 digits to the right of the decimal point.
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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30 Nov 2011, 04:43
3
(1/5)^10 is (0.2)^10

we know that 2^5=32 .we have (2^5) *(2^5) or 32*32=1024 since we have 10 zeros , our result is
0.0000001024

so 10th digit is 4
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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30 Nov 2011, 04:52
VeritasPrepKarishma wrote:
feruz77 wrote:
Hi fluke,

but, inasmuch as I know tenth digit to the right of the decimal point is a first number after the decimal point. Please correct if I am wrong!

You are talking about the 'tenths' digit which is right after the decimal point.
'The tenth digit to the right of the decimal' is the digit that appears after 9 digits to the right of the decimal point.

Hi Karishma,

Thanks for reply. Such kind of things make GMAT very tricky. I appreciate your help.
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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30 Nov 2011, 22:31
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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12 Dec 2011, 22:47
Hi Karishma,
Thanks for making it clear . very confusing language.
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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28 Dec 2013, 03:06
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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30 Dec 2013, 13:30
1
gmatpapa wrote:
What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

Yeah actually 1/5 = 0.2 = 2*10^-1

so 2^10 * 10^-10

2 has sequence 2,4,8,6.

Hence digit will be 4

Hope it helps

Cheers!
J
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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26 Aug 2015, 08:07
so, this is about Tenth vs Tenths! Tricky
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What is the tenth digit to the right of the decimal point  [#permalink]

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16 Aug 2017, 20:38
1/5=0.2
Now the question becomes what is 10th digit of (0.2)¹⁰
for calculation remove decimal
2X2X2=8-a
2X2X2=8-b
(2X2X2)X2=8X2-c
8X8=64-a&b
64X8X2=1024-a&b&c
10th place after decimal
0.0000001024
Ans=4
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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31 Aug 2017, 20:39
jlgdr wrote:
gmatpapa wrote:
What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

Yeah actually 1/5 = 0.2 = 2*10^-1

so 2^10 * 10^-10

2 has sequence 2,4,8,6.

Hence digit will be 4

Hope it helps

Cheers!
J

hi

is it possible to find out the tenth digit of the expression without further simplification made to "2^10"....?
anybody out there ....?

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What is the tenth digit to the right of the decimal point  [#permalink]

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27 Sep 2018, 15:24
1
Analysis (30 seconds): The question is asking me to find the 10th digit of $$0.2^1^0$$, the answer choices look familiar, possibly the pattern of final digits for powers of 2. I have absolutely no idea how to calculate the actual value of this so I'm going to go ahead and assume two things : 1) I can ignore the fact that the number is a decimal and focus on the 2, and 2) the 10th digit is actually the last digit (because I'm confident GMAC don't actually want me to compute the value of $$0.2^1^0$$). In order to solve this I'll quickly refresh my memory on the pattern of end digits for powers of 2 and then see what the 10th power would yield.

Strategy: Find the pattern, Count to 10

Find the pattern (30 seconds):
$$2^0 = 0$$
$$2^1 = 2$$
$$2^2 = 4$$
$$2^3 = 8$$
$$2^4 = 16$$
$$2^5 = 32$$
Looks like the pattern is: [2,4,8,6] with the exception of 0.

Count to 10 (10 seconds):
Using [2,4,8,6] as the pattern and starting from index 1 I can see that the 10th power will give me an end digit of 4.

Total Time: 1:10
What is the tenth digit to the right of the decimal point   [#permalink] 27 Sep 2018, 15:24
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