HW 1_solutions.pdf - MATH 472 002 Solutions of Homework 1...

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MATH 472 002: Solutions of Homework 1Fall 2017Problems1. (10 points) Section 0.2, Exercise 8 (c), (d)Proof.(c) Definea:= (0.001)2.Then23a= (1.001)2= (1)2+a= (1)10+a, equivalently(23-1)10·a=1. Therefore,a=(17)10. Calculate now(111)2= (1·22+ 1·21+ 1·20)10= (7)10.In total,(111.001)2= (7 +17)10= (507)10.(d) Definea:= (0.01)2.Then22a= (1.01)2= (1)2+a= (1)10+a, equivalently(22-1)10·a= 1.Therefore,a=(13)10. Calculate now(1010)2= (1·23+ 0·22+ 1·21+ 0·20)10= (10)10.In total,(1010.01)2= (10 +13)10= (313)10.
3. (10 points) Section 0.5, Exercise 7Proof.
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