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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, 03:37
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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
[Reveal] Spoiler: OA

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

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18 Feb 2011, 04:41
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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, 05:38
(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, 04:09
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, 04:53
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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, 05:43
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(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, 05:52
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, 23:31
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown [#permalink]

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12 Dec 2011, 23:47
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, 04:06
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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, 14:30
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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, 09:07
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, 21:38
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, 21:39
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 ....?

Re: What is the tenth digit to the right of the decimal point   [#permalink] 31 Aug 2017, 21:39
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