We have the following sentences:
- Someone might have a million GBP in the bank.
- There are over 7 billion people in the world.
- The US current debt is over 20 trillion USD.
What do all these numbers have in common? They are big. When reading about them, that is the only similarity. A million dollar company is worlds apart from a billion dollar company. During conversations, a million, a billion and a trillion all sound the same.
What can be done?
There is a way around this problem. We have well-developed intuitions about smaller numbers: they appear frequently in our life. We can also convert giant numbers to smaller numbers by thinking of magnitudes, or even simpler, how many digits the number has, i.e. we use Scientific Notation by default.
And what do I do with that?
Now that we have numbers written in magnitudes, we can easily compare them. For example, if our unit is euros, we can consider which items are in a given magnitude:
| Magnitude | Value | Examples |
|---|---|---|
| 1 | 10 | Cost of a meal, public transportation ticket |
| 2 | 100 | Clothing |
| 3 | 1,000 | Furniture, rent, plane tickets |
| 4 | 10,000 | Family holiday |
| 5 | 100,000 | Car |
| 6 | 1,000,000 | House, wealth of smaller companies |
| 7 | 10,000,000 | Launch of a reusable space rocket |
| 8 | 100,000,000 | Airplane |
| 9 | 1,000,000,000 | World population |
| 10 | 10,000,000,000 | Ethereum’s Market Cap |
| 11 | 100,000,000,000 | Cost of the British National Health Service |
| 12 | 1,000,000,000,000 | Value of assets managed by the world’s largest hedge fund |
| 13 | 10,000,000,000,000 | National debt of the United States. |
Every time we see a new number, we can think about where it lies in this magnitude list and compare it to what we already know. That way when we see that a million dollars were spent on a new car fleet for government officials, hopefully we’ll realise that a million is about the correct value for such a fleet, instead of being outraged at the sound of a million dollars being spent by the government in something apparently unnecessary.
Can you build a detailed magnitude list for yourself?
A Clever way to estimate with large numbers
This Ted-Ed Video shows this concept in action. Enjoy!