16) Decimal Expansion [16 Marks, 4 for each part] 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 9 ? K = 1 b) Let {bn} be a sequence with bn E {0, 1, 2, . ..,9}. Let In = 2 bk 10 k . Show that {rn} is nondecreasing and bounded above by 1. Note: This shows that {rn} converges and that if B = lim rn, then BE [0, 1]. c) Let a E [0, 1]. Define a1 = max {k E {0, 1, 2, ...,9} | 16