Summary

Data scientists are confronted with both the problems, rounding errors, and instabilities because of numerical precision problems.

In R, one should be aware that printing a result does not mean that you see the exact number. It's just rounded off on given digits (default = 7), but internally, the numbers are saved with more digits.

In any case, we saw in this chapter that the floating point arithmetic of a computer cannot represent all numbers, and almost every number is rounded to the next even digit. By reading this chapter, you learned the basic knowledge of machine numbers and rounding. This knowledge is mandatory for any data scientist and statistician although these problems play a minor role in the following chapters. We also saw in this chapter convergence issues: how to observe convergence for a given problem. This will be continued and extended in the following chapters, such as in Chapter 4, Simulation of Random Numbers, and Chapter 5, Monte Carlo Methods for Optimization...