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What is the 21st digit of the decimal [
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29 Sep 2018, 09:19
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47% (01:42) correct 53% (02:19) wrong based on 43 sessions
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Senior DS Moderator
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WE: Business Development (Energy and Utilities)

What is the 21st digit of the decimal [
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29 Sep 2018, 21:53
Official Solution: \(\frac{1}{111} + \frac{1}{37} + \frac{1}{27} + \frac{1}{9} + \frac{1}{3}\) = \(\frac{9}{999} + \frac{27}{999} + \frac{37}{999} + \frac{111}{999} + \frac{333}{3999}\) = \(\frac{517}{999}\) = 0.517517517... It is clear that 7 at places 3rd, 6th, 9th... multiple of 3. Hence 21st digit is 7 Answer is CMethod to convert fraction (with only 9 as digits in denominator) to decimal  If the fraction is abc/999, decimal will be 0.abcabcabc...
We need to just repeat the numerator indefinitely after the decimal.  if the fraction is ABC/99999, decimal will be 0.00ABC00ABC
We need to add zeros after zero at the start of numerator and repeat it indefinitely.
gmatbusters wrote: Weekly Quant Quiz Question  5 What is the 21st digit of the decimal \(\frac{1}{111} + \frac{1}{37} + \frac{1}{27} + \frac{1}{9} + \frac{1}{3}\) ? a) 5 b) 6 c) 7 d) 8 e) 9
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Re: What is the 21st digit of the decimal [
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29 Sep 2018, 09:27
1/111+1/37+1/27+1/9+1/3= .009 + .027+.037+.111+.333 = 0.xx7 as the 3rd is 7 the 21st is also 7 ==> Ans C
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Re: What is the 21st digit of the decimal [
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29 Sep 2018, 09:34
This can be written as  13/27 + 4/111 = 0.0360360360... + 0.481481.. = 0.517517 Hence, 7
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Re: What is the 21st digit of the decimal [
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29 Sep 2018, 09:35
1/111+1/37=4/111=21st and 22nd digit=6,0 1/27+1/9+1/3=21st and 22nd digit 1,4 Answer=7(1+6)
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Re: What is the 21st digit of the decimal [
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29 Sep 2018, 11:11
1/3 = 0.3333(non terminating)
Thus, 21st digit is 3
1/9 = 0.11111(nonterminating)
Thus, 21st digit is 1
1/27 = 0. 037037
Thus number repeats in sequence of 3 digits  037, thus 21st digit number is 7
1/37 = 0.027. Thus, same as above, 21st digit is 7
1/111 = 0.009, thus, for same reason as above, 21st digit is 9
Adding above, 3+1+7+7+9 = 7
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Re: What is the 21st digit of the decimal [
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29 Sep 2018, 14:11
Expressing each of the fractions in the decimal form:
1/3 = 0.333333333333.... > 21st digit is 3 1/9 = 0.111111111111... > 21st digit is 1 1/27 = 0.037037037037...> 21st digit is 7 1/37 = 0.027027027027.. > 21st digit is 7 1/111= 0.009009009...... > 21st digit is 9
9+7+7+1+3 = 27, 7 is the 21st digit and 2 is carried over for sum in 20th digit.
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