Why would you ever trade in motes for useless strange coins? Need them to infuse, and for reputation. Motes=legendary gear.
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Well if you have 100+ strange and they are barely used for anything anymore besides leveling up gear, you can trade them in if you're a bit short on strange coins for when xur rolls around. I know they are more common in strike playlists now, but since they took away the weekly heroic, I've found that myself, and a few of my friends have been only a few strange coins away from the minimum cost of gear from xur.
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100+ motes*