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Why 5000 mAh rather than just 5 Ah?
Batteries often have a rating like 3250mAh, which is arguably clearer than 3.25Ah, especially on a datasheet.
And I think it gets more obvious once you compare two phones and see which one to buy. I can tell you immediately, between a battery with 3450mAh and 4200mAn there's a 750mAh difference.
But i have to look twice at the numbers if it's 3.45Ah and 4.2Ah and i want to see if it's worth the extra $70.
How is it arguably clearer?
It's only clearer to absolute mongloids that can't get their head around the idea of "bigger number better!".
Sorry, I basically combined two separate thoughts in a weird way. First, I meant that the raw battery cells themselves are usually rated in mAh on their datasheets, so manufacturers simply kept using that unit on their marketing material. Second, I meant that datasheets usually use mAh because it is a more appropriate unit than Ah for comparing cells of that approximate size. This is somewhat common in engineering documents - you will often see measurements written as 20.0mm instead of 2.0cm (usually because it is more consistent with the rest of the documentation). In this case it's because many of the Li-Ion cells used in phones will have their charge/discharge ratings in mA, so it makes sense to have the capacities in the corresponding mAh.
But I do agree, on marketing material it makes much more sense to just write the capacity in Ah (or better, Wh). Using mAh just because it's a bigger number is plain silly.
Marketing, it just sounds better. Any other answer is just an excuse.