Need help with ways to visualize 1,000,000

In My Humble Opinion
21

[QUOTE=Zeldar]
I know you’ve asked for ways to cope with a million but I once worked out how to deal with a nanosecond which was staggering to me.

A nanosecond is to a second as a second is to 32 years.

That’s billions and is way more impressive. But a million seconds runs into 11 days (as Duckster noted upthread). Still a decent lump of time.
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The late Admiral Grace Hopper used to hand out pieces of wire just under foot long, that being the distance that light would travel in a nanosecond.

22

I like Hampshire’s idea. If you want to use the paper to full effect (keeping in mind the proportions of an 8.5" x 11" piece of paper), make your grids 88 x 113, print a hundred of those, and you will have one million squares with an error factor of approximately 1/3 of a percent.

23

[QUOTE=Noone Special]
To visualize how little a million can be, have them visualize a stack of playing dice, say each is 1 cm[sup]3[/sup]. Now imagine* a stack of these, 100 across, 100 deep and 100 tall – or 1 m[sup]3[/sup].

This stack of dice – which fits easily within a room – will contain 1,000,000 dice.
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Here’s an alternative way for them to visualize how little a million can be.

Have them visualize a ~3,000 sq. ft. home. Then say, “This is about the equivalent of 1 million dollars in Southern California. Not very much at all, huh?”

24

[QUOTE=Hampshire]
Make a 100 x 100 grid of Xs or Os on an excel spreadsheet.
Highlight the entire grid and print “selection” and “fit to 1 page”.
This will give you 10,000 Xs or Os.
Print 100 copies.
Lay the copies on the floor in a 10 x 10 grid.

There’s your million Xs or Os.
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Very nice answer. I just did it. The 100 pages are printing now.

25

A cube of 100 on a side has a volume of 100000. Could you get a million BBs or something like that?

26

Turn it into a fund raising drive for your school… try to collect a million pennies ($10,000)
it works out to about 3-1/2 40 gallon drums

be carefull where you put it, though, it weighs about 2 1/2 tons

Regards
FML

27

Yone Minagawa, the oldest living person in the world, is just over one million hours old.

28

If you hire 10 young shaved strippers each with a full head of hair, they will have a combined one million hairs, not counting peach fuzz. This always goes over well with community college kids. It would even be better if you brought the strippers to class.

29

Here’s a spatial method involving marbles…

Take a million 1" diameter marbles, and form a cube: each edge is 100 marbles long, the cube is contained in a cube with volume 1000000 cubic inches, which is a cube 100 inches (~8 feet) per edge. So basically, 1000000 marbles, each with diameter 1", form a cube that is approximately 8 feet per edge. It’s actually more like 8 feet, 4 inches on each side. But it’s a pretty good physical image of a million.

30

Here’s a spatial method involving marbles…

Take a million 1" diameter marbles, and form a cube: each edge is 100 marbles long, the cube is contained in a cube with volume 1000000 cubic inches, which is a cube 100 inches (~8 feet) per edge. So basically, 1000000 marbles, each with diameter 1", form a cube that is approximately 8 feet per edge. It’s actually more like 8 feet, 4 inches on each side. But it’s a pretty good physical image of a million.

1 marathon = 26.2 miles @5280 feet per mile = 138336 feet 1000000 feet = 7.228776313 marathons

You can also think in terms of one foot steps in a marathon … You’d need to run approximately 7.3 full marathons to get 1,000,000 feet.

31

If you have an 1024x768 monitor, that has about 800,000 pixels on it. If you have a 1280x1024 monitor, it has about 1,300,000 pixels on it. Open up MS paint and make a single pixel black.

32

In case you haven’t seen it, there’s an impressive documentary involving a class of school kids in Whitwell, Tennessee, whose teacher came up with an amazing demonstration of the six million lost during the Holocaust. It’s called Six Million Paper Clips and is definitely worth more than just a demo of big numbers.

33

[QUOTE=interface2x]
One girl, in particular, I was able to dissuade after three days when she was three pages in at 1,000 and I mentioned that she only had to do that 1,000 more times.
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This suggests a possibility.

At the beginning, you could say, “I have a challenge for somebody. You will get two hundred and fifty dollars if you succeed. Do I have a volunteer?” Make a show of holding up a pre-written check, or cash even.

(By the way, if the amount is too large, like a thousand bucks, they’ll know you’re not serious. It has to be small enough that it looks like you’re just barely willing to pay it out if somebody “beats the odds” and succeeds, but large enough to serve as an enticement.)

When somebody stands up, say, “If you can write out, by hand, the numbers from one to five thousand before this lecture is over, I will give you this check.” Adjust for other durations.

Anyway, whatever they manage to complete in the time period, do a quick bit of math, and show their highest number as some tiny fraction of a million, with appropriate extrapolation for how long it would take to get there.

Basically, the applicable rate is not how many numbers one is capable of writing per some time frame, but how many individual digits one can manage. In other words, it takes twice as long to write down 11 as it does to write 1.

So with a little preparatory work, you could get some baselines for reference. It takes 180 digits to write 10 to 99; 2700 digits to write 100 to 999, for a total of 2889 individual digits so far. 38,889 digits to write everything up to 9999; 488,889 to write everything up to 99,999; and 5,888,890 total digits to write down everything from 1 to 1,000,000. Assuming an insanely fast and basically unsustainable rate of two digits per second, that’s (scribble scribble scribble) about 34 days. The reality, of course, will be far longer.

This gives you an easy laugh throughout the presentation. At various intervals, you could check in with your erstwhile volunteer. “Hey, there, Steve, how you doing? Three oh six, man, you’re gonna need to step it up there, Steve-O. Come on, folks, let’s give him some encouragement, he looks like he’s getting tired. Steve-O! Steve-O!” And so on.

Anyway, finally, at the end, you could say, “Okay, in an hour, you managed to get to, what? Okay, 1497. At that rate, if you didn’t sleep, eat, or go to the bathroom, it would take you 164 days to write the numbers from one to a million. Good luck with that.”

Or, alternatively, you could ask the volunteer to suggest a target. “You definitely won’t make it to a million in an hour. Do you think you could make it to a hundred thousand? Probably not. Ten thousand? Well, give it a shot and we’ll see how you do.”

Just a thought.

34

“out, by hand, the numbers from one to five thousand” Finished! Where’s my money? That was easy. :wink:

35

A stack of a million sheets of paper would be (very) roughly 250 feet tall - 25 stories tall.

36

Have them calculate the number of days since they were born. At age 20 it will be somewhere around 7300. Then ask them to compute how old they will be after living one million days. 2739 years! :eek:

37

I often use examples like these to explain to my friends and family just how hard it is to win lotto jackpots:

“Ok, you have 1cm cubes. stack them in a giant cube, 100x100x100. Now stack 13 more giant cubes like that one. Take one 1cm cube off the top of one of the giant cubes and paint the 1cm cube black. Ok, now throw the whole entire lot, single black cube included, into a giant bin and mix it all up. Reach in there and, without looking, grab the black cube by itself. You get to do this once a week.”