Here's the test:
Take a piece of blank paper. Draw a dot on the left and mark it “0”. Draw a dot opposite the first one, on the right, and mark it “1,000,000,000” (one billion). Draw a line between the two dots. That's a number line, like many of us learned in school. It represents all the numbers between zero and a billion, with the integers equally spaced. Now draw a third dot on the line where you think the number 1,000,000 (one million) belongs.The report I read said that about half of people trying this test put the third dot in roughly the correct place; everyone else got it wrong. That's the result I was skeptical of. The correct place, of course, is 1/1000th of the line's length from the left. So if your line was 10 inches long, the third dot would be a mere 1/100th of an inch from the dot for zero.
So I've tried the test now on five people (a ludicrously small sample, I know), more or less randomly selected. None of them were even remotely close to the right answer. The most common place for the third dot was somewhere near the middle of the line. One person put it about 1/5th of the line's length from the right! I'm slightly comforted by the fact that none of these people were scientists or engineers ... but only slightly comforted.
I find this absolutely stunning. Somehow it never occurred to me that so many adults – probably a majority of adults – wouldn't intuitively grasp such basic concepts. That level of innumeracy means that things like discussions of government budgets are beyond their ken, as they don't understand the significance of the difference between millions, billions, or trillions of dollars (and probably not thousands, either!). Or basic astronomical concepts. Sheesh, much of science involves numbers covering multiple orders of magnitude.
Gobsmacked, I am...