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Irrational Numbers

D is a real n...

Question

D is a real number which noon terminating digits a1 and a2 after the decimal point. Let D= 0.a1 a2 a1 a2........with a1 and a2 both not zero which of the following when mutiplied by D will necessarily give an integer?

Options:

18

198

125

75

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Solution

Option B

D=0.a1 a2 a1 a2....= 0.a1 a2 (1+0.01+0.01^2+....+0.01^n+.....)

D= 0.a1 a2 (1/(1-0.01))=0.a1 a2 /0.99=(a1 a2)/99

so, integer should be k99. therefore, B 198=299
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