Floating point

Floating point numbers allow both large and small numbers to be represented in a small amount of memory by keeping a binary fraction and an exponent. This makes them very useful, however they are not without some interesting problems.

Floating point issues

At first this seems nonsensical:

    $ tmp = 0.1 + 0.1 + 0.1 == 0.3
    "[tmp]"

False

In decimal it seems obvious that the result should be True. Floats work with binary fractions though, and there isn't a precise representation of 0.1, just a in decimal there's no precise representation of one third. These approximations tend to be hidden when printing floating point numbers as rather than printing all the digits, values are rounded. So while two numbers may look the same when printed their values are different.

Another surprise awaits with this code:

    $ tmp = 2.0 ** 53
    "[tmp:,f]"
    $ tmp += 1
    "[tmp:,f]"

9,007,119,254,740,992.000000
9,007,119,254,740,992.000000

Surely the second number should be one bigger than the first? The problem here is that with numbers this big the next value is actually 2 higher, so no matter how many times 1 is added the result doesn't change.
See Floating point issues  for more information.

Special numbers

In addition to the numbers you might expect there are some special values:

+0, -0

There are two zeros, a positive one and a negative one.

inf, -inf

There are two infinity values, a positive and a negative one.

nan

This stands for "not a number" and can result from nonsensical operations like trying to multiply infinity by zero.

Float literals

A floating point number has either a decimal point . or an exponent e or E, or both. The exponent may have a sign + or -. Underscores _ may be used to group digits.
See Python: floating point literals 

Comparing floats

In general, due to the issues above, avoid comparing floats for equality or inequality using == and !=. Two floats that ought to be the same, and print the same, may have differences in their actual values. If you absolutely must compare floats consider using math.isClose()