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Plain Talking About Numbers

Andrew Elliott

I've recently been taking forward an idea that's been in the back of my mind for a while: www.IsThatABigNumber.com is a website that has a simple aim: to put big numbers in context, and in so doing, start to develop a more intuitive feel for them.

While I can intellectually understand the meaning of large numbers, typically written in scientific notation (e.g., 2.5 x 10^8 or expressed in billions and trillions), that's not quite the same as having a "feeling" for very large numbers. In fact, when I really think about it, I think my sense of comfort with numbers runs out somewhere around the 1000 mark. That is, I think I can visualise 1000 items without things becoming blurry, but not much more than that.  But that is another blog post for another day.

The topic for today is how we talk about numbers. The website IsThatABigNumber.com is all about numbers, and the expression of those numbers needs to be clear and comprehensible.

Take measurements of length: I was taught about the SI system, based on meters, kilograms and seconds. Now for scientists and engineers, it's perfectly fine to talk about 4 x 10^7 m. It's convenient for calculations and it's the proper thing to do. But if I want to explain how long the equator is, I want to about 40 thousand kilometers instead.

Because? Because that's the way folk talk. Not 4 x 10^7 m; not 40 Megameters; not even 40 million meters. In my mind, things that can be measured using "meters" as the unit range from a bit less than one meter, to a somewhat more than a thousand. Half a meter? 0.5m is just fine; a 10,000m race? That's fine too. 50,000m? Nah, I'm better with 50km; 0.02m? Nope, give me 2cm or 20mm.

So, here are some of the principles that I am using for IsThatABigNumber:

For all numbers)

  • Numbers are expressed in three parts: a base magnitude between 1 and 1000, followed by a multiple, and where needed, a unit.  So the population of the world is expressed as 7 billion, not 7,000,000,000 (all those zeroes? too hard to grok)
  • The multiple used is based around powers of 1000, with the exception that ...
  • "12,500" is more natural than "12.5 thousand", so for numbers in the 1000 - 999,999 range, we make an exception and use numerals
  • But "12.5 million" is more natural than 12,500,000, so for a million and beyond, we use "*illion" words, to the limit of septillion - 10^24 (and I struggle with septillion!)
  • Beyond septillion, fall back to scientific notation starting with 10^27. In this area, the game is pretty much out of the hands of "folk", and in the hands of the scientists.

The, when it comes to units: for distance measures:

  • Meters are used between 1m and 999m
  • Kilometers are used for distances above 1km
  • Millimeters are used for distances below 1 m.

For measuring mass:

  • Kilograms are used for masses above 1kg
  • Grams are used for masses below 1 kg
  • (Thinking about using metric tons - 1000kg for bigger masses - but currently undecided)

Time is a whole separate problem, not yet addressed.  For now, years are the only units in use, but really, days and seconds seem more natural for small time periods. But then this is about BIG Num8ers.

Money is the other measure included in IsThatABigNumber.com. For now, US Dollars are the standard unit, rendered with a "$" sign.