[thinkingeric]

"teach them to estimate"

I suspect that the 'calculator age' has caused kids (and kids that have now grown up to be parents) and maybe educators to over-value an increase in significant digits in calculations. It's interesting that the method of multiplication illustrated in the article is referred to as 'new' since when you use a slide rule, you operate in this way anyway. And to echo Hans Bethe, this is often "good enough".