[londons_explore]

It's understandable - you trust a tool like a calculator to give you the right answer. If it sometimes makes mistakes and you have to check each answer by hand, it isn't really saving you any time.

To many, a rounding error makes the answer "wrong", and suddenly the tool has switched from a reliable one into an untrustworthy one.

[dahfizz]

> you trust a tool like a calculator to give you the right answer.

By middle school, kids should have learned that you can't trust calculators. There are all sorts of numbers like pi, e, sqrt(2) that are impossible to represent. Once you start getting into trig, you have to accept rounding.

[aaaronic]

Sure, but .1 is definitely representable, so they can be excused for finding it a little unreasonable that .1+.1+.1+.1+.1+.1+.1+.1+.1+.1 doesn't equal 1 in many languages.

Explaining _why_ .1 isn't representable requires explaining IEEE-754 and explaining _that_ requires an understanding of binary numeric representation.

I teach college students who find this confusing, so I think it's fair that the average person finds floating point behavior confusing (in fact, I've had to explain to Physics Professors doing computation simulation work why their 1-<tiny number> isn't working out the way they expect -- though they initially tried using double doubles to get around the problem).

[chrchang523]

This does depend a bit on the calculator. embedded_hiker's anecdote has made me update in the direction of exposing my daughter to Wolfram Alpha before Python...

[jdmichal]

My AP calc teacher was an expert on writing tests that would trigger calculators into approximation mode. Pretty much every homework problem, the calculator could easily do an exact answer. But you better have learned, because come test time, the best your calculator is going to offer is 0.942858934759084...