Yeah, those. Well, they ain’t perfect. In fact, they can be downright inaccurate at times.
First off, what floating point numbers actually are. They’re basically a way for computers to represent decimal values using binary code (which is just 1s and 0s). This might sound simple enough, but there’s a catch: not all decimal values can be represented exactly in binary form.
For example, let’s say you want to represent the number 0.375 as a floating point value using 8 bits (which is what most computers use for single-precision floats). Well, that’s impossible because there are only 2^8 possible values with 8 bits, and none of them exactly match 0.375.
So instead, the computer has to round it off or truncate some of the digits in order to fit it into a binary format. And this is where things get interesting (or frustrating, depending on how you look at it).
When you do math with floating point numbers, there’s always going to be some level of error involved because they can only represent certain values exactly. For example, let’s say you want to calculate the sum of 0.1 + 0.2 using single-precision floats (which is what most computers use by default). Well, that might not give you the exact answer you were expecting:
0.3000000476837158203125
Yep, that’s right there’s a tiny bit of error involved in this calculation because 0.1 and 0.2 can’t be represented exactly as floating point values using only 8 bits (which is what most computers use for single-precision floats). And if you do more complex math with these numbers, the errors can compound over time until they become significant enough to affect your results.
So how can we deal with this? Well, there are a few things you can do:
1) Use higher precision floating point values (like double-precision floats or even quadruple-precision floats if you’re really serious about accuracy). This will give you more bits to work with and reduce the errors involved in your calculations.
2) Avoid using floating point numbers for tasks that require high levels of accuracy, like scientific computing or financial analysis. Instead, use fixed-point arithmetic (which is basically just integer math) whenever possible.
3) Be aware of the limitations of floating point values and take steps to mitigate them in your code. For example, you can add a small amount of error tolerance to your calculations to account for the fact that they won’t be exactly accurate due to rounding errors.