Examples of negative numbers can obviously be found in real world applications where we might consider the outside temperature during a cold winter's day, which has dropped below freezing. We could then calculate how much the temperature has dropped from the previous day's recording, which was a much warmer day. 

There may also be occasions where the height of a mountain is required and the base is below sea level. To understand the true height, we would have to add the height above sea level to the depth of the base, which is below sea level.