I had an engineer who worked for me back in the 90s who always had the best BS detector. After enough instances to convince me this wasn’t just accidental I mentioned it to him and he grinned and said it was something he prided himself on.
The reason turned out to be his dad, who was an electrical engineer too, had not only been a good mentor but had strictly enforced the “no calculator” rule for all his kids, and instead taught them to use a slide rule just like he’d done years prior. That taught him to always think in “orders of magnitude” because that’s what you have to do with a slide rule, and he just generalized the same approach to non-math subjects. One brother was a contractor but he said the same discipline had saved him countless hours and thousands of dollars by being able to spot something that didn’t make sense early.
I learned to use a slide rule in a Navy electronics school in 1962 but no one spoke of “orders of magnitude” back then, the term was “scientific notation” or “powers of ten”. One thousand was 10 to the third power, one million was ten to the sixth power etc., each power of ten merely meant one more zero to the left of the decimal. Of course no one actually said power it was simply “ten to the sixth”. A fractional figure was simply a negative power of ten, one thousandth became “ten to the minus third”. Each negative power simply added a zero to the RIGHT of the decimal. It was decades later when I first heard “order of magnitude” and I had to figure out what it meant.
That kind of training is probably the main reason I want to puke when someone utters a mathematical absurdity, in fact a mathematical impossibility, such as “five times less” or even worse “five hundred percent less”. That kind of garbage is in daily use by people who definitely should know better.
I do believe that learning the slide rule helps a person learn to spot gross errors such as appear often in news reporting, it is quite common to see orders in decimal placement. I learned long ago that in any news report that includes numbers that can be compared for accuracy there is usually at least one mistake. Percentages seem to be particularly baffling to people and are very often computed wrongly. People who intend to deceive should make every effort to avoid using numbers if at all possible.