How can 1,000,000,000 be demonstrated?

Question

Can you suggest some object large enough that a single one can be seen but small enough that one billion of them can be gathered in one place in a reasonable and practical way?
As a teacher, I would like to demonstrate to students how extremely huge 1,000,000,000 is. A physical example is the best way to do this.

Answer 1

You need 1000 x 1000 x 1000. A billion 1-mm cubes would pack into a cubic meter. That would be some pretty coarse sand, but I'm sure the students could find some grains that well-represent a cubic millimeter (salt or sugar are way too fine).. Get out your meter stick to demonstrate that 1 cubic meter is not really very big. That's just a thousand layers of a million square millimeters. A good lesson in dimensional scaling is the area which that billion-grain cubic meter would cover if it were spread into just one layer at one millimeter high, i.e. 1000 square meters, maybe a quarter of a soccer field. Going to one dimension, line up those grains end-to-end a billion millimeters long, and the trail will stretch a thousand kilometers. These are, of course, just thought experiments.

How huge is a billion? Here's a calculation to make you nervous. You can't see heartbeats, but they are easy to count. Ask the kids if they think the teacher's heart has beat a billion times. (We hit that mark in our mid-twenties.)

Answer 2

the first answer that comes to mind is sand - a single grain can be seen by your eye, and yet a beach is made up of billions of grains of sand.
now, when we begin talking about moving this stuff, that gets more complicated. From this artcile (http://www.reefs.org/library/article/r_toonen23.html) the average grain of a particular brand of sandbox sand is 338.51 micrometers in diameter. Doesn't sound like much, but a billion grains of that sand would take up about 90 cubic meters, or over 3,000 cubic feet of space. To put that in perspective, if your classroom is 20 feet wide, 30 feet long, and 10 feet high, the sand would fill up just over half of that room - maybe practical to do with a backhoe or a dump truck.

Answer 3

One idea might be time: Its an easy reference to how much time one second equals... Have students guess at how many years 1,000,000,000 seconds equals (approximate). The answer is 31.71 (approximate).

Another idea may be money: No you may not be able to show them a $1billion, however...again, they do understand time...how long would it take to spend $1 billion if you spent $1000 per week or per month... Example: You could spend $1million per year, for 83.3 years...

Or yes still, you could keep hunting for the visual example.

Sand would probably work...the challenge would be calculating the volume of a billion grains of sand...the diameter ranges from 2mm to .05mm Still some how I think that if you could accomplish that....1 billion grains would be a manageable quantity.

Answer 4

There are about a billion grains of sand in 5 cubic meters... about the size of a vw beetle.

Answer 5

A running track with ten one-metre-wide lanes and 100 metres long will contain 1000 000 000 square millimetres.

A millilitre of water weighs one gram. 1 000 000 000 of these takes up 1 000 cubic metres and weighs 1 000 tonnes.

You should be able to show them something from these examples.

Answer 6

Use a grain of sand versus a sand truck
Use a drop of water versus the ocean
Use a person versus the solar system

Answer 7

i think it is slightly too large to physically represent, something about 0.1X0.1X0.1mm would still fill 1 cubic metre. a good example would be that the earth's orbital circumference isn't even 1,000,000,000 km

Answer 8

My science teacher in high school had a jar that held one million tiny beads in it. the jar had several different colors in beads on it. The colors where used to demonstrate parts per million. I think he bought it on-line from Edmund Scientific. I also saw this book that might be helpful:
How Much Is a Million?, Vol. 1
by David M. Schwartz, Steven Kellogg

Answer 9

Well... you can take the example of sand and sand particles or tell them about water and water drops etc.,

Or stars.

Answer 10

Being a teacher, you should have the brainpower to figure this one out yourself.