We all know what a million is: it is a big number. Yet we use it quite a lot in our day to day. But how big actually is it?
Let’s start by asking a seemingly innocent question: how long would it take you to count to a million?
Take your wild guess and write it down quickly! A couple of hours? 10 hours? 3 years? Maybe more?…

Did it? let’do the maths then…

First, lets assume you can count 1 number per second… what? you think you can go faster?… 1,2,3,4,5,6,7,8,9,10…

ok ok… I see you can’t count very fast but let me ask you to count from 435.231 up… 435.232, 435.233, 435.234…Ummmm not so easy is it? I am sure it took you more than a second to say any of those numbers numbers!
Aha! So you believe I may have picked 435.231 just for this to happen, surely…After all there is a lot of numbers you can say in less than a second that come to your mind right now, right? And 435.231 may just be an exception to those.

And here it comes the first insight into how big is a million… Let’s assume you can say all numbers of 5 or less digits in less than a second (you may even find this is challenging.. Try 15.578…but I am magnificent and accept that you could do it easily), and that those of 6 digits in more than a second. How would that equate?

Well it is not difficult to see that there is 9 times more numbers of 6 digits in a million than numbers of 5 or less!!!! For each number you can come up of 5 digits I have 9 by only adding a digit 1-9 in front…

So maybe I have to review my average estimate to more than a second per number after all… 😜

But no worries, I hope you are convinced (and happy) that a number per second is a good assumption on the average speed a human can count.
So that gives us the 1.000.000 seconds to complete our counting.And how long is that? Not difficult maths gives us :

Without eating or sleeping or even stopping for a wee…

So yes a million is bigger than we usually think it is…

Great video from Vlog Brothers

Other links:

Visualise a million

Quick guess from Veritasium

Visualising one million digits of π


One thought on “How big is a million?

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