Errors: Finite Precision Algebra Consider a "FAKE" computer that rounds any real number into the 3-significant figure, floating- point decimal format t d.dd x 10ds, where each d is a decimal from 0-9, but there are no other restrictions (no "infinity", no "forcing a number to be denormal if the d in the exponent is 0"). (a) What is the largest number (realmax) you could store in this FAKE computer? (b) What is the smallest positive number (realmin) you could store in this FAKE computer that is 2.1 5 pts not denormal (i.e. maintains all 3 significant figures)? (c) What is the value of machine precision (e)? Now let's say you want to add the following four numbers with this FAKE computer: (d) What is the final value of S in the fake computer if you did the sum in the left-to-right order (e) Demonstrate the ideal order you should add the four numbers to provide the most accurate S 1.4317341.3 6.41 (The real, exact sum is clearly 222.14) written above? What is the percent error in the value of S (compared to the real sum)? value of S. What is that final value of S, and what is its percent error? Errors: Finite Precision Algebra Consider a "FAKE" computer that rounds any real number into the 3-significant figure, floating- point decimal format t d.dd x 10ds, where each d is a decimal from 0-9, but there are no other restrictions (no "infinity", no "forcing a number to be denormal if the d in the exponent is 0"). (a) What is the largest number (realmax) you could store in this FAKE computer? (b) What is the smallest positive number (realmin) you could store in this FAKE computer that is 2.1 5 pts not denormal (i.e. maintains all 3 significant figures)? (c) What is the value of machine precision (e)? Now let's say you want to add the following four numbers with this FAKE computer: (d) What is the final value of S in the fake computer if you did the sum in the left-to-right order (e) Demonstrate the ideal order you should add the four numbers to provide the most accurate S 1.4317341.3 6.41 (The real, exact sum is clearly 222.14) written above? What is the percent error in the value of S (compared to the real sum)? value of S. What is that final value of S, and what is its percent error