What’s a slide rule and how are they so useful?

In: 11

Let’s say you want to multiply 43 x 89, but you don’t have a pen and paper, and you don’t have a calculator. Are there any mathematical tricks we might be able to use as shortcuts?

One is using properties of exponents and logarithms. 10^x * 10^y = 10^(x+y), no matter what x and y are. 43 is 10^1.663, and 89 = 10^1.949, so 43 x 89 = 10^(1.663 + 1.949).

A slide rule is a set of wooden or plastic rulers with logarithm tables visually printed on them. You would slide one piece representing the 89 to line it up to where another piece says 43, so that their lengths are back to back. Then you’re able to see what number is at the tip, and it is their product.

It looks super complicated at first, but ultimately it lets you multiply or divide any two numbers just by lining up special sticks and not needing to actually do calculations.

It’s basically a manual calculator. It lets you do division and multiplication (and sometimes square and cube roots depending on the design) before digital calculators were widely available.

If you think of a regular ruler, you an see how you could use two rulers to add…put a 2″ ruler with a 4″ ruler and you’ve got 6″. 2 + 4 = 6.

Slide rules do the same idea, except they’re marked in a particular way (not every interval is the same length) so that “adding” lengths on a slide rule works out to multiplication. “Subtraction” does division. This uses a branch of math called logarithms…there are other good ELI5 posts on that if you want to know more.

They’re useful because, if you’re proficient, they’re very fast and they don’t need any batteries or anything. And, when they were in common use, regular calculators either didn’t exist or were ludicrously expensive. A slide rule, even a really good one, is comparatively cheap.