Gifted Issues Discussion homepage Forums General Discussion Semi-wonkish question about significant figures

So. I have a question about math education and significant figures.

My kids are coming home with decimal addition problems that look something like this:

  3.1416  
+2.71828

The teacher, the math books, and many internet sites all say that you should do the addition by tossing in a zero, as follows:

  3.14160  
+2.71828

I disagree. I think that "tossing in a zero" is one of those little details that seems so reasonable yet creates a blurry picture of mathematics (and science) and can lead to real problems down the road. Bottom line IMO: you don't know if that "6" in 3.1416 is 0.00055-9 being rounded up or 0.00060-4 being rounded down. So yes, you can toss in a zero, but not knowing anything else about the number, you have at best a 1/10 chance that your answer is correct in the 5th decimal place past the zero. And of course, the result in the 5th decimal place can affect the 4th decimal place and so on.

I don't think it's appropriate to be teaching the finer points of significant figures to kids learning about decimals for the first time. However, I do think it's easy to tell the kids, "You don't know if that 5 is 0.00057 rounded up or 0.00064 rounded down or just plain 0.00060. All of those different numbers will give you different answers when you add. So you should only add the numbers you're sure about, which is only as far as the ten-thousandths place. Just discard any decimal digit past the ten-thousands place in the other number." This approach would also tie in nicely with rounding.


This method, IMO, sets kids up to have a more intuitive understanding of significant figures and why they're important.

Thoughts? Am I wrong?