16) Decimal Expansion Note: In this question we are going to see how to use the MCT to build a decimal expansion for every real number in [0, 1]. a) What is K=1 10 ? b) Let {bn} be a sequence with by E {0, 1, 2, ...,9}. Let my = _ 105- Show that {n } is nondecreasing and bounded above by 1. Note: This shows that {} converges and that if B = lim In, then BE [0, 1]. 71 00 c) Let a E [0, 1]. Define a, = max {k E {0, 1, 2, ...,9} | 16 ai 1= 1 i) If a = #, what is an? What is s1? ii) If a = I, what is as? What is s;? d) Given a E [0, 1] and { sn } as defined above, show that lim s, = Q. 12-+00