Sometimes we cannot express a value exactly with a finite
Chapter 7, Problem P7.23(choose chapter or problem)
Sometimes we cannot express a value exactly with a finite number of decimal or binary symbols. For example, we have 1/3 = 0.333333 or 4/33 = 0.12121212 in which the overbar indicates that the pattern repeats indefinitely. a. Convert 0.110 to binary form indicating the repeating pattern with an overbar. b. Repeat for 0.610. c. Perform the calculation (0.1 1024 102) 10 4 on your calculator. This should give the exact result, namely zero, because most calculators use BCD and the arithmetic is essentially decimal in nature. d. Repeat the calculation of part (c) with MATLAB. The result is not exactly zero because the calculations are carried out in binary with a finite number of bits, resulting in an approximate representation with roundoff error for 0.1. This error is magnified in the calculation
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