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What is the tenth digit to the right of the decimal point
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18 Feb 2011, 02:37
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51% (01:16) correct 49% (01:08) wrong based on 1045 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
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18 Feb 2011, 03:41
\((\frac{1}{5})^{10}\) \(\frac{1}{5^{10}}\) \(\frac{1}{(\frac{10}{2})^{10}}\) \(\frac{2^{10}}{{10}^{10}}\) \(\frac{1024}{{10}^{10}}\) \(1024*10^{10}\) \(.0000001024\) Tenth digit to the right of decimal is 4. Ans: "C"
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown
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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
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30 Nov 2011, 03:09
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
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30 Nov 2011, 03:53
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
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30 Nov 2011, 04:43
(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
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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
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30 Nov 2011, 22:31
I made a silly mistake...



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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown
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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
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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
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30 Dec 2013, 13:30
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 Answer is C Hope it helps Cheers! J



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Re: What is the tenth digit to the right of the decimal point
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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
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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=8a 2X2X2=8b (2X2X2)X2=8X2c 8X8=64a&b 64X8X2=1024a&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
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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 Answer is C 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 ....? thanks in advance ...



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What is the tenth digit to the right of the decimal point
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27 Sep 2018, 15:24
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.
Answer = C Total Time: 1:10




What is the tenth digit to the right of the decimal point &nbs
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