## Math Tricks for Kilograms and Pounds

### 2018-02-10

I’m going to share some math tricks for converting between kilograms and pounds, something I often deal with when weightlifting. This post is long, but if you stick around to the end, I’ll share the super secret divisibility rule for 11. (Originally posted to Facebook. Reposted on my blog at Jim Campbell’s suggestion.)

If you find a mathematician or engineer who’s good at doing math in their head and ask them how they do it, you’ll find they have a handful of techniques they apply in different situations. Many of these techniques involve turning problems into things we’re already good at. What are we good at? Well, multiplying and dividing by 10 is trivial. It’s just moving a decimal point. And most of us are pretty good at doubling and halving things. So, multiplying and dividing by 10 and 2 are sweet spots.

1kg is approximately 2.2lb. (If you need better precision, use a computer.) So to convert kilograms to pounds, we have to multiply by 2.2. Let’s pull out that distributive law. 2.2x = (2 + 0.2)x = 2x + 0.2x = 2x + (2x)/10. We’ve reduced the problem to multiplication by 2 and division by 10.

“Woah Shaun, stop with the algebra!” OK. Take the kilograms. Double it. Take that double, shift the decimal place. Add the double and the decimal-shifted double. For example, take 150kg, a respectable squat weight. Double it = 300. Divide by 10 = 30. Add these two together = 330lb. (Google will tell you the answer is 330.693lb.)

But what about converting pounds back to kilograms? Do we have to divide by 2.2? That sounds awful. But division by 2.2 is multiplication by 5/11. Does that make it any better? Yes! Really? YES! Division by 11 is awesome, and for some reason, nobody learns it in school.

To divide by 11, first divide by 10. That’s your current total. Divide that by 10 and subtract the result from the current total. That’s your new current total. Divide that by 10 and add it to the current total. That’s your new current total. Continue dividing by 10 and alternating addition and subtraction. Do this until you die of exhaustion, you see the two-digit repeating pattern, or you’re happy with the precision. Recall that 2.2 was only an approximate conversion to begin with, so I stop when all the action is after the decimal point. Round whole numbers are good enough for me.

But we needed to multiply by 5/11, not just 1/11. No worries. To multiply by x/11, instead of starting with 1/10, start with x/10. Luckily, 5/10 is just 1/2. We like dividing by 2.

My body weight is about 190lb. What is that in kilograms? Half of 190 is 95. Divide by 10 for 9.5. Subtract 9.5 from 95 for 85.5. Divide 9.5 by 10 for almost one. Addition is next, so let’s call it 86kg. (Google will tell you the answer is 86.1826kg.)

So there you go. Quick tricks to help you get approximate conversions between kilograms and pounds in your head.

But what about the super secret divisibility rule for 11 I promised? It follows the same pattern as the technique I gave for dividing by 11. Just do alternating addition and subtraction on the digits of a number. If the result is divisible by 11, so is the original number. Is 1936 divisible by 11? 1-9+3-6 = -11. It sure is.

Eleven is awesome.

*tap* *tap* *tap* testing testing *tap* *tap* *tap*

Still here? Cool. Here’s a bonus tip that wasn’t in my original post. All that stuff about 11? It works the same way for whatever number “11” happens to represent in any radix. Need to divide by 11_8 (decimal 9) in octal? Same division algorithm. Need to check divisibility by 11_16 (decimal 17) in hexadecimal? Same division rule. Looking for some fun weekend math? Take a look at the divisibility rules you know, figure out why they work, and use that to figure out what divisibility rules you have in other bases. Hint: every divisibility rule I can name stems from three basic kinds of tests.