Binance has added a new feature that will allow you to convert the fragments of dust left over from trades, small airdrops, and referrals into BNB.
I hear the team has built a broom, who wants it?
— CZ (@cz_binance) April 24, 2018
For the time being, it seems the feature is only on the desktop website. To convert your dust into BNB, go to the page Estimated Values where it shows your balances for all coins. You may have to uncheck the Hide box to show all balances under .001 BTC.
Select the Convert To BNB tab which will lead you to another page where you can select which coins you’d like to convert. You can convert balances with a valuation below .001 BTC to BNB only once every 24 hours.
After selecting which coins you’d like to convert, scroll to the bottom of the page which will tell you how much BNB you will receive, and click exchange. It does seem the feature is a little buggy at the moment and may take a few times for the transaction to go through as it’s most likely overloaded. Waiting and refreshing a few times seems to help in order to make the transaction go through.