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22 Oct 2019, 03:22
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (01:50) correct
36%
(01:21)
wrong
based on 572
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If 359/1650 = 0.2175, what is the 100th digit to the right of the decimal point of the fraction?
A. 1
B. 2
C. 5
D. 7
E. 9
A. 1
B. 2
C. 5
D. 7
E. 9
22 Oct 2019, 21:23
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Bunuel
\(\frac{359}{1650}=\frac{359*2}{1650*2}=\frac{718}{3300}=\frac{718*3}{3300*3}=\frac{2154}{9900}=\frac{21.54}{99}=\frac{21}{99}+\frac{0.54}{99}=0.212121..+0.0054545=0.21757575...\)
We should be aware that when divided by 99 the numerator (<99) repeats itself. For example - 22/99=0.22.. and 2/99=0.0202..
In 0.217575.. even place in decimals will always be 5
C
22 Oct 2019, 19:31
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Cyclicity of recurrence decimals of 1/3 is 1
Cyclicity of recurrence decimals of 1/11 is 2
Cyclicity of recurrence decimals of 1/3*11 is LCM(1,2)=2
the 100th digit to the right of the decimal point of the fraction is 5
Or
\(\frac{359*6}{1650*6}\)=\(\frac{2154}{9900}\)= \([21+(\frac{75}{99})] * 10^{-2}\)= .21757575757575......
100th digit to the right of the decimal point= 5
Cyclicity of recurrence decimals of 1/11 is 2
Cyclicity of recurrence decimals of 1/3*11 is LCM(1,2)=2
the 100th digit to the right of the decimal point of the fraction is 5
Or
\(\frac{359*6}{1650*6}\)=\(\frac{2154}{9900}\)= \([21+(\frac{75}{99})] * 10^{-2}\)= .21757575757575......
100th digit to the right of the decimal point= 5
Bunuel
