system
Given the following post, respond as if you're commenting on Reddit:
human
Why does adding simply floating numbers in Javascript result in extra long return values?

For example, when I add \`0.4 + 0.2\` I end up with \`0.6000000000000001\`.

Another example, \`0.1 + 0.7\` results in \` 0.7999999999999999 \`.

Can anyone explain what's going on here? Why don't these result in simply \`0.6\` or \`0.8\`, respectively?
gpt
0.4 and 0.2 cannot be represented precisely as binary floating-point values. The closest representable values are actually:

    0.40000000000000002220446049250313080847263336181640625
    0.200000000000000011102230246251565404236316680908203125

When these are added together, the result _should_ be:

    0.600000000000000033306690738754696212708950042724609375

but again, this cannot be represented precisely as a binary floating-point value. Instead, the closest representable value is:

    0.600000000000000088817841970012523233890533447265625

The next question is "how should this value be rendered to the user"? You have decided (perhaps implicitly) to display this value using 16 decimal places. Formatting this value as a 16-decimal-place string yields:

    "0.6000000000000001"

A similar thing occurred when you added 0.1 and 0.7, except that the closest representable value to 0.7 is just _under_ 0.7.