Hi everyone, I've been lurking in the background for some time now and thought I should let you know I was here. The topic of rounding is an opportune topic to introduce myself.
My name is Kate Jones and I am a PhD student in physics at the University of New England in Australia. I also teach maths at the local TAFE (Technical and Further Education) College.
Scientists use 'formal' rounding all the time when they consider the accuracy of a measurement or the uncertanties associated with an experiment.
Example: radius of a circle = 2 cm therefore circumference = 12.56637061436 cm (from calculator). That number of decimal places is nonsensical, so what do I round to? The answer depends on the equipment that you used to measure the radius. Use of a metre ruler with, at best, a minimum reading of 0.1 cm means you should round to 1 d.p. However, if you had used a micrometer with a minimum reading of 0.001 you can round to 3 d.p., always using 'formal' rounding rules. Rounding is also important when dealing with irrational numbers and the level of accuruacy you want in your calculation.
With maths and science being closely related I am sure this is why rounding and sig. figures are dealt with at secondary school. If you have adult learners with thoughts of gaining certificates in general education and then moving on to university then formal rounding should be taught. I really can't justify teaching this type of rounding to adults who want to survive in the 'real' world.
Some other thoughts on the topic - most examples in the discussion so far have been with rounding up in real life (e.g. money problems) how about the case when you have a packet of 19 sweets that must be shared EQUALLY among 4 children. 19/4 = 4.75 but we would round down and give each child 4 sweets and mum and dad would probably share the remainder. Also, in Australia, our lowest monetary denomination is the five cent piece,5c. At the cash register 91c or 92c would be round down to 90c; 93c and 94c are round up to 95c; 96c and 97c are round down to 95c and 98c and 99c are round up to $1. Interesting!