> we're pretty good at understanding "big" numbers, say somewhere between a million and a billion.
When we stop and think about it, maybe. But try this experiment with a friend (or a few times with different friends): take a sheet of A4 or "letter" sized paper and a pencil, turn it in landscape orientation and mark the far left side of it with '0', and the far right side as '1B' telling them it's an even scale from zero to one billion, and ask them "without thinking about it just mark where a million would be." -- it's important to get a response from "the top of their head" to understand the difference between what we can recall, and what we habitually think. Most people are way off. If paper isn't handy use fingers and a large object you can touch - e.g. top edge of monitor or TV etc.
Dividing in half 10 times comes pretty close (976562), but kinda defeats the point of getting a spontaneous answer as the what they feel it would be. On a 1 meter scale the 1 million mark would be just 1mm along. On a piece of paper, it's virtually indistinguishable from the starting point.
The point of the exercise is that many people don't really grok that a billion is a thousand times bigger than a million, - or rather just how much bigger a factor of 1000 actually is, when talking about big numbers that they're not as used to... no matter whether using paper, or a desk, or a wall for scale.
When we stop and think about it, maybe. But try this experiment with a friend (or a few times with different friends): take a sheet of A4 or "letter" sized paper and a pencil, turn it in landscape orientation and mark the far left side of it with '0', and the far right side as '1B' telling them it's an even scale from zero to one billion, and ask them "without thinking about it just mark where a million would be." -- it's important to get a response from "the top of their head" to understand the difference between what we can recall, and what we habitually think. Most people are way off. If paper isn't handy use fingers and a large object you can touch - e.g. top edge of monitor or TV etc.