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<p>It’s a bit like long division; You start with the decimal and put commas after sets of two digits both to the left and right of the decimal. But unlike long division you keep doubling the divisor and add an extra digit to the divisor at the end for each operation. Hard to explain without a diagram, but it’s there. The sad thing for us was when we were taught this, probably in 7th grade, it was like how a computer is taught by a programmer. The teacher just focussed on the steps and didn’t take the trouble to explain why it works, which is really a nifty application of basic algebra, and we were too dumb to ask.</p>
<p>As far as the current generation’s reliance on calculators, it’s really double edged. The one who isn’t interested in math learns even less math now; however the kid who has mastered math can tackle much more complex problems in engg/applied math without being bogged down by an uncooperative integral or whatever - a bit like saying the astronaut of today uses computers to fly the shuttle but may lack the skills needed to fly the Wright bros’ plane.</p>