String To Float Issues

All digital computers that I am familiar with are binary. The results you got are not what you expected or wanted, but are correct. When you are working with floats and doubles, you should generally consider that you are working with approximations. Machine representations of numbers and machine arithmetic aren't quite the same as the real thing.

In base 10 you cannot write 1/3 exactly in the form of a terminating decimal fraction. In the same way, you cannot write any fraction with a denominator that is not a power of 2 exactly in the form of a terminating binary point fraction. There are also other artifacts involved in working with binary machine floating point numbers.

If the artifacts of machine floating point arithmetic are not acceptable in your application, then you will have to use something other than floats or doubles.

One alternative might be to use scaled integers. Another is to use an arbitrary precision math package of some type.

What to use depends on the situation you are dealing with and what matches up best with the different ways of representing numbers with a machine.

Floats have about 6 digits of precision. However, they are stored similar to scientific notation. It stores a number along with a magnitude to set where in that number the decimal point should appear. For example, you could have the number 654321 and then adjust it by placing the decimal point in the middle (654.321), before the beginning (0.000000654321), or after the end (654321000000). However, you only get about 6 digits to store the precision of that number. If you want more precision, you can use a double instead of a float. Doubles have about 15 digits of precision. For more information, see this.

As the other answer said, you can use a library that stores numbers as fractions. That way, you can have virtually unlimited precision. Just keep in mind that these numbers take up more memory and are slow to use. You'll have to do some searching, but here are some starting points so you know what to look for: an extended decimal class, and a fractional numbers class.

Once you do math, the results will be inconsistent. There's an article about it here on Codeproject.

Reliable Floating Point Equality Comparison[^]

If the language you're using has a decimal type, use it instead of floats/doubles, because using a decimal type for math that could result in "floating point" values retains its accuracy. It's a little slower, but if accuracy is "your thing", it's a better choice.