I encountered a particularly nasty bug or effect and tracking it down and correcting it is going to be extremely annoying.
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I intended to send it from one of the two active addresses in the wallet but inadvertently left the default app selected to Any Address. Nevertheless, even if that were a contributing factor by pulling inputs from multiple addresses the problem is in rounding up the amount sent. That output amount to the destination address should not be changed. Additionally, there was no verification of inputs and outputs like the browser based.
I reported this one a while ago. The mobile app rounds sent amounts to six decimal places. I think it should be considered a serious issue because it can mess up a lot of use cases where sending an exact amount is important.
(The Google docs thing is irrelevant, the reason it displays weird amounts is because it's internally handling floating point data types which are suited to represent approximations but not exact values.)