More seriously, although I agree with the underlying point that approximation and sane treatment of significant figures should be treated better in school, I do think that this way lies madness.

What you're going to end up with is children thinking (correctly, in your world) that you can only add numbers if they have the same number of digits after the decimal place. Sure, you can define addition that way, and provided we have ways to coerce numbers into having the right number of decimal places, all will be well. But the children will now not be able to add 1 to 2.5 without first turning 1 into 1.0. If this were proposed in Everyday Math, imagine the outrage.

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