# Division of Powers of Ten is wrong. Why?

I’ve encountered an error that caused me a lot of grief, can somebody explain why:

julia> (10^18)/(10^22)
0.5362758289192254


The fix was:

julia> (10.0^18)/(10.0^22)
0.0001


but i do not see how it ended up with such a wild solution.

It’s not the division that was “wrong,” it was the exponentiation.

julia> 10^22
1864712049423024128


This is because Julia uses machine integer arithmetic — see:

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Thank you,
Edit: Yes there is. It is called safe integers.

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As someone else has explained, 10^18/10^22 produces integer 10^18 divided by integer 10^22. Because 10^18 can be represented correctly by 64 bit integers while 10^19 and larger numbers are too big for 64 bit integers (and hence cause overflow), number 10^22 overflows and becomes ca. 1.86\cdot 10^{18}.

If 10^N or 10^N is meant to be a real number as in scientific notation, the “correct” syntax in Julia, MATLAB, Python, etc. is keN = k\cdot 10^N (i.e., if you want to use Float64). And then you’ll get the result you probably expect:

julia> 1e18/1e22
0.0001
julia> typeof(ans)
Float64


If you want Float 32, the syntax for k\cdot 10^N is kfN.

Personally, I don’t think this is a problem at all — as long as one realizes that scientific notation is supposed to be written keN etc. — if anything, it is more systematic than in MATLAB and other languages.

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let me know if you have any questions regarding https://github.com/JeffreySarnoff/SaferIntegers.jl

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