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A company wishes to distill a 0.830 mole fraction ethanol (0.170 mole fraction water) solution. To aid in the distillation process, a 0.950 mole fraction benzene (0.050 mole fraction water) mixture containing fresh benzene and a recovered benzene solution is added.
In this section, we will explore exactly when the expansion of decimal of a rational number is terminating and when it is non-terminating repeating. 1) 0.125 = 125/1000 = 125/10 = 5 /(2 x 5 ) = 1/2 2) 0.00134 = 134/100000 = 134/10 = (2 x 67)/(2 x 5 ) = 67/(2 x 5 ) 3) 0.7 = 7/10 = 7/(2 x 5) Note : As we know that 2 and 5 are the only prime factors of 10. 1) Theorem 1: Let x be a rational number whose expansion of decimal terminates.