- 1)
- (6 pt) Consider the list of numbers below:

1.777 0.003692 113.9 0.01992 34.39 0.5438

- a)
- What is the exact sum of these numbers?
- b)
- Add the numbers from largest to smallest using 4 digit chopped arithmetic. What is the relatve error in the result?
- c)
- Add the numbers from smallest to largest using 4 digit chopped arithmetic. What is the relatve error in the result?
- d)
- Which of parts b) or c) above gives the most accurate result? Explain why one method has a smaller relative error than the other.
- e)
- Based on your results, what is the most accurate way to add a series of numbers?
- f)
- How would your answer to part e) change if you had both positive and negative numbers?

- 2)
- (6 pt) Solve the linear system below using 4 digit,
chopped arithmetic. Compute the relative error in the final solution.
How does your
relative error compare with the examples done in class?

The exact answer is

*x*= -1,*y*= 1. - 3)
- Suppose you have a computer designed with the
following specifications:
- Base = 3
- Digits of accuracy = 4
- Exponent range = [-2,2]

- a)
- (1 pt) What is the largest positive number that can be represented?
- b)
- (1 pt) What the smallest positive number that can be represented assuming a standard normalizing rule?