## Decade dollars and using the right level of precision

A couple of years ago I was referring a article about a company which had seen tremendous growth in a very short period of time. It was a Swedish company that had somehow established itself in Russia but with very little exposure in the Swedish press at all. A guy asked me, surprised at not having heard of this company, how many employees they had. My answer? I think it was 500, but it could have been 50.

500 or 50. That's a magnitude in difference, yet what stuck was the digit 5, which was clearly not the most significant piece of information. If i had said roughly 100, or 30-100 employees that would have been way more valuable. Most of the time we don't need the precision, and the precision can be misleading too, indicating that we have precise measurements when in fact we have none. What can we do about this?

One idea is to use a logarithmic scale, something that is used a lot already in many scientific fields. Instead of thinking of the number of employees as 50 or 500, you would instead think of it as 2 or 3, which is log10 of each number rounded to the closest whole number. You don't actually have to do the operation in your head though - all you have to is to count the number of zeroes in a number, and then round up if the first digit is roughly more than 3 (or, to be precise, the square root of 10).This might sound complicated, but after a while it's pretty easy to do quickly. In the case of 50, you see that there's a trailing zero and 5 is "kind of a big number" so that literally turns it into 1+1=2.

Many things in life exist both in the very small and in the very large. Humans simple don't have a frame of reference for many of the things we encounter in modern everyday life. Someone who's 150 cm long is short and someone who is 220 is tall, but what's the difference between a millionaire and a billionaire? A star and a galaxy? Most of us don't have good references for these things.

There are plenty of things we would be happy with just an approximate idea of the magnitude of something, and where more detail would cloud our view: Speed. Size. Distance. Time. Money. Population. Twitter followers. Page views. Book sales.

Let's have a look at a money, and more specifically on a unit I choose to call decade dollars. These are very rough estimates, and some of them might even be misleading, but they give you an idea of scale and a way to compare things.

0dd - coffee
1dd - lunch
2dd - phone
3dd - mac
4dd - old car (or minimum wage salary for a year)
5dd - average USA house (or a year in hilton)
6dd - central pied-a-terre
7dd - private jet (or fu money)
8dd - Hollywood A-list net worth
9dd - Forbes 400
10dd - Forbes 100 (or yearly budget of NASA)
11dd - Bill Gates
12dd - UK GDP
13dd - US GDP
14dd - World GDP
15dd - Now that's just too much

Some of you might have noticed that this is very similar to scientific notation on the form 5e^2,but without all the cruft and extra precision. Remember, the point is to get a rough idea of a large number.

Don't mistake 500 for 50, or worse, 7 billion for 7 million. Instead, cut back on your precision.