When HP sell you a new printer (D1660) they only give you starter cartridges with it which hold a very small amount of ink in them Hp 300 black 4ml and the Hp 300 6ml colour cartridges. I was using about 3 black and 2 colours cartridge per month and it was costing me a small fortune. I later found out that Hp do a higher yield versions of the 300 cartridges which cost only a few pounds more but hold far more ink in them than the starter cartridges which I was using before. What you need is a HP 300XL on the black which hold 12mls of ink rather than the 4mls of ink that is in the 300 starter black cartridge and for the colour you should be using the HP 300XL colour cartridge which holds 11mls of ink rather than the 6ml HP choose to put in the starter. I can even go one better, I now use a company called advantage online who stock the Hp originals plus do a British premium compatible 300XL bk and 300XL colour cartridges which hold 18mls black and 18mls colour. I have used them a couple of times so far and have been quite impressed. I hope you don't fall into the Hp trap of selling a very good printer (Deskjet D1660) at a very cheap price and then trying to charge you load of money for starter cartridges.
Blooming things last about 5 minutes, I wish I had brought a different printer. The cartridges are very small so don't hold much, and if left in the printer dry out very quickly, so I had to removed and put into air tight plastic box between use.
This cartridge performed adequately until about half of its ink had been used. Then I got a message that the HP Deskjet F2480 printer that I was using it on deemed it to be incompatible. Are you sure that is indeed an HP 300 Black ink cartridge?