ALT title: the gaps between floats panel 1: floating point numbers have to fit into 32 or 64 bits This means there are only 2^64 64-bit floats, the same way there are only 2^64 64-bit integers panel 2: this means floating point numbers have to be spread out you can imagine them all spaced out on a number line, like this: (picture of a bunch of lines, with small gaps between them. The gaps are smaller on the left and bigger on the right) panel 3: the gaps start small. the next 64-bit float after 1.0 is 1 point (lots of 0s) 2 the gap between these two floats is 0 point (lots of 0s) 2, or 2^-52 gaps are always a power of 2 panel 4: the gaps get bigger as the numbers get bigger the next 64-bit float after 1000000000000000000 is that number plus 16384. so the gap is 16384, or 2^14! panel 5: the gaps make calculations inaccurate when you do math on floating point numbers, you might have to round the result small mistakes can add up panel 6: this inaccuracy is inevitable (...)