The decimal number 0.1 has an infinitely repeating binary fraction.

Consider how 1/3 in decimal is 0.33333… If you truncate that to some finite prefix, you no longer have 1/3. Now let’s suppose we know, in some context, that we’ll only ever have a finite number of digits — let’s say 5 digits after the decimal point. Then, if someone asks “what fraction is equivalent to 0.33333?”, then it is reasonable to reply with “1/3”. That might sound like we’re lying, but remember that we agreed that, in this context of discussion, we have a finite number of digits — so the value 1/3 outside of this context has no way of being represented faithfully inside this context, so we can only assume that the person is asking about the nearest approximation of “1/3 as it means outside this context”. If the person asking feels lied to, that’s on them for not keeping the base assumptions straight.

So back to floating point, and the case of 0.1 represented as 64 bit floating point number. In base 2, the decimal number 0.1 looks like 0.0001100110011… (the 0011 being repeated infinitely). But we don’t have an infinite number of digits. The finite truncation of that is the closest we can get to the decimal number 0.1, and by the same rationale as earlier (where I said that equating 1/3 with 0.33333 is reasonable), your programming language will likely parse “0.1” as a f64 and print it back out as such. However, if you try something like (a=0.1; a+a+a) you’ll likely be surprised at what you find.