What does it mean when we give lots of decimals behind the degrees?

Many of us have GPS devices which give us locations in decimal degrees, but what do all those decimals really signify and can we rely on them? In the image below, Alex Rebelo has set out a series of increasingly accurate data points (using Kenilworth Race Track in Cape Town as his example). 

You can clearly see here the difference between giving two decimal places and three decimal places is about 1km!

Should you ever give 5 decimal places? Unless you are using a survey GPS, the answer is no. 

Most handheld GPS units can get an accuracy of around 6-8m, so giving 4 decimal places is realistic. For most of our purposes (usually mapping frogs), this accuracy level is fine.