3.2 pts Fundamentals of (A)-type Finite Precision Errors (Short - 1 point per question, but you STILL have to show all your work and reasoning!) a) Express the number 49526.84 as a floating-point decimal number. b) Express the number 6.5 x 108 as a fixed-point decimal number. c) Pretend you have a FAKE computer that works in floating-point decimals (instead of binary), and you type "eps" in MATLAB and get the value eps = le-4. i. Calculate the error in storing the exact number 463987.21596. ii. Draw the "discrete number line" starting from the exact number 9999.5 and continuing on to the next-largest nine numbers (so you end with a total of 10 numbers). d) Now pretend you have a FAKE computer that stores numbers in floating-point decimal form d.ddd x 10(+ d), where each of the five "d's represents a digit between 0 and 9. Determine the Finite Precision error in calculating X = log10(2.003) - log (2.001) in the standard "left-to-right" order (i.e. first determining log10(2.003), then rounding that to storable form, then determining log10(2.001), then rounding that to storable form, then subtract those two numbers, and round that to storable form for the final answer X). Optimize the calculation for X so that you get a much smaller Finite Precision error on the same computer. What is that final error? (i.e. show me a "better" way of calculating X, and then do it and calculate the error. Hint: look at HW2.) e) Use the same computer as part d. (i.e. 1 d.ddd x 10(d) to add the following set of numbers: X = 996.3 +0.3485 +4.356 +0.2405 + 0.09486 +0.1865 +0.4000 i. Determine the Finite Precision error in calculating X if you do the sum in the order given, from left-to-right. ii. Optimize the order you do the calculation for X so that you get the smallest Finite Precision error on the same computer. What is value of this "optimal" error? How much smaller is it than the error from e(i) above? Honestly - go back and look at your answers for these short questions. Make sure you SHOW YOUR WORK! For example, if you just drew a number-line in c(ii) and didn't explain to me why you have the spacing between numbers that you do, and how that exact spacing comes from the given value of e, then go back and re-do that problem properly so you get full grades. Same for all the problems