Round Numbers: An Introduction to Numerical Expression (UMAP)

In this module the notions of precision (absolute error) and accuracy (relative error) are introduced in the context of representing meaured and approximate quantities. Scientific notation, significant digits, interval arithmetic, and standard rounding procedures for use in various computational situations are explained. Warnings are included about traps to avoid in making certain calculations and numerical representations. Students learn to appropriately treat approximate numbers as opposed to exact ones, and to properly use approximate numbers in calculations and representaions of results.

Table of Contents:

1. INTRODUCTION

2. SCIENTIFIC NOTATION

3. SIGNIFICANT DIGITS

4. ROUNDING

5. CHOPPING

6. ACCURACY VS. PRECISION

7. COMPUTATIONS WITH ROUND NUMBERS

8. WARNINGS

9. SUMMARY

10. MODEL EXAM

11. ANSWERS TO EXERCISES

12. ANSWERS TO MODEL EXAM