Accurately Converting Units Involving Extremely Small Numbers?

Jun 16, 2014

I need to convert units accurately. Some of these units include angstroms (0.1nm) and astronomical units or light years. I can't seem to accurately perform these equations (probably mostly because of lack of a proper conversion formula). For example:

1 angstrom = 1.79985601 × 10^-14 leagues (or, 0.00000000000001799856 leagues).

To perform the conversion right now, I'm simply multiplying the angstroms by 0.00000000000001799856. However, inputting 55560000000000 (angstroms in one league) results in 0.9999999936. Why is this? Is it possible to work around it? I believe there's a term for the inability for a computer to process 1/3rd properly, but I can't remember what it's called - is that the problem?

I am using BigDecimals for all equations.

Edit: a mod can change the title if they think another is more fitting.

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[Code] .....

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Here is the code I have typed so far.

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The server code:

package Chatroom;
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[code]....

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Original JavaScript

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