Sous Vide temperature accuracy
Most home kitchen immersion circulators advertise that they are accurate in the .1 to .3 degree F range.  Practically speaking, if you were considering a home-made device, you can easily get away with less accuracy than that.  So, .5 would be just fine.  In a pinch, I've used a pot of water and a thermometer, turning the gas on an off.  Not very convenient, not very accurate, but it can work with close monitoring.  By the way, I do sometime set my circulator to .5 degree increments, but, honestly, that's probably more obsessiveness than is required.