In today's lecture we saw why real-valued (floating-point) numbers are used very rarely, if at all, in systems programming and operating systems kernels. Here's an article describing the problem, Stop Using Floating-Point Numbers to Store Money https://spin.atomicobject.com/floating-point-numbers/ and another going into several pages of detail: What Every Programmer Should Know About Floating-Point Arithmetic https://floating-point-gui.de

A student recently emailed me with this related question. Thought the answer may also interest others. ___ Hi Dr.McDonald, I got a question out of interest inspired by a lab question. We know that calculating the floating number is inaccurate in computer. I was thinking how the computing software works like Mathematica, which is wildly used in computing area and its really powerful. I also known Mathematica is written in C and Java. So, how do we solve this kind of problem caused by floating numbers. ___ There's a number of libraries, and programming languages, that support what's termed multi-precision arithmetic, or arbitrary precision arithmetic, supporting both 'infinitely large' integers, and floating-point values with an 'unlimited' number of decimal places. Often these libraries will recognise standard values, such as e, sqrt(2), and 1 / pi as exact values, and perform their arithmetic using symbolic computation, where they can, rather than converting the values to imprecise approximations. Here's a good list: https://en.wikipedia.org/wiki/List_of_arbitrary-precision_arithmetic_software Here's an example of using the standard bc utility to calculate the first 1000 digits of pi: time bc -l <<< "scale=1000;4*a(1)" Hope this helps,