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Comment by haberman | Hacker News Reader

The precise value of double(0.1) is 0.1000000000000000055511151231257827021181583404541015625. That is precise, not an approximation.

If you know of a program in any of these languages that will print this value for "0.1" using built-in functionality, please let me know because I would love to know about it.

Likewise the precise value of double(1e50) is 100000000000000007629769841091887003294964970946560. Anything else is an approximation of its true value.

In another message you said that what's really important is that the string representation uniquely identifies the precise value. While that will help you reconstruct the value later, it does not help you understand why 0.1 + 0.2 != 0.3.

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Python does it:

  >>> from decimal import Decimal
  >>> Decimal(0.1)
  Decimal('0.1000000000000000055511151231257827021181583404541015625')
  >>> Decimal(1e50)
  Decimal('100000000000000007629769841091887003294964970946560')

Great to know, thanks!

Haskell will tell you that

    toRational 0.1 = 3602879701896397 % 36028797018963968
    toRational 1e50 = 100000000000000007629769841091887003294964970946560 % 1

Both of those values are precise, although I admit the first isn't really useful for human beings.

The easiest way to see this exact value in Julia is to convert the Float64 value 0.1 to BigFloat and then print that:

    julia> big(0.1)
    1.000000000000000055511151231257827021181583404541015625e-01

    julia> big(1e50)
    1.0000000000000000762976984109188700329496497094656e+50

Note that this is exactly why you don't normally want to construct BigFloats this way. Instead you want to do this:

    julia> BigFloat("0.1")
    1.000000000000000000000000000000000000000000000000000000000000000000000000000002e-01

    julia> BigFloat("1e50")
    1e+50

It helps because 0.1 + 0.2 produces 0.30000000000000004 for 64-bit floats – so at least you can see that this value isn't the same as 0.3. In Ruby you just get two values that print the same yet aren't equal, which is way more confusing. I agree that printing the minimal number of digits required for reconstruction does not help with explaining why 0.1, 0.2 and 0.3 in 64-bit floats aren't the real values 1/10, 2/10 and 3/10.

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