How Big is a Million REALLY:

For many years we tried to find a way to illustrate just how big one million is.  It is our strong belief that most normal folks do not have any true conception of how BIG this number is.

Our first idea was to Xerox a $1 bill and copy it a million times, cut these out and stack them in a room so that everyone who came in could actually see a "million bucks".

We began to plan this idea:
We Xeroxed the bill:
dollar.jpg (12374 bytes)
Next  we copied it 6 times and arranged them on a sheet of Xerox paper.  When we divided 1,000,000 by 6 we realized that it would take 166,667 sheets of paper to make the bills.  Now this is more than half of the entire year's supply of paper at our local Middle School!

So we shrunk the bills and tried to fit 20 miniature bills on each sheet.  Then we only needed 1,000,000 / 20 = 50,000 pieces!  So we started to figure out how long it would take to cut them out with a paper cutter.

We figured we could cut out 5 sheets of 20 at one time, or 100 dollars in about 27 seconds.  So we would need 10,000 sets of those 100 dollars to get all million bills cut.  Each of those 10,000 sets takes 27 seconds to cut, for a total of  27,000 seconds. 

So how long is 27,000 seconds?  Well there are 60 seconds in a minute so 27,000/60 = 450 minutes.   And since there are 60 minutes in an hour, we get 450 / 60 = 7.5 solid hours of cutting! That is without a single moment of break!

Well we still thought that maybe if students helped it would work.  Then we began to figure out how much space it would take to display the bills. 

One ream of paper holds 500 sheets and is 2in x 8.5in x 11in or 187 cubic inches.  This is a little more than 1/10 of a cubic foot of space.

Now, let's see...... each sheet has 20 dollars on it, so we need 1,000,000/20 = 50,000 sheets.  Each ream of paper holds 500 sheets so we need 50,000/500 = 100 reams of paper.   Since each ream is 1/10 of a cubic foot the total space needed to store the bills was 100x1/10 or 10 cubic feet. 

We didn't think that was too bad, until we figured out how much it would weigh!  Each ream weighs 7.25 pounds so the total weight of this exercise would be 100 x 7.25 or 725 pounds of fake dollar bills.

Finally, we gave up on the $1 bill idea and moved on to other things.  We thought about collecting items throughout the year and trying to get a million that way.  However, every idea we came up with was just too big to fit into a classroom.

We read about a school that collected bottle caps all year long.   They stored them in their gym but had to quit before they were near their goal because the gym was getting too crowded and the building was in danger collapsing because of the added weight placed on just that one section of the gym floor.

For a couple of years we gave up on the idea of "seeing" a million of something.  We continued to let our students think of a million as nothing more than a 1 with 6 zeros after it.

Then one day while reading a book by Marylyn Burns called I Hate Mathematics! Book (Brown Paper...  when we came across this picture,

dots.gif (4513 bytes)

Well there are 1,105 dots on this picture.  we figured if we copied it 905 times we would have 1,000,025 dots.   We were able to fit 8,840 dots on each page of Xerox paper.  It took 1,000,000/8,840 = 113.1221719... or 114 sheets of Xerox paper to print the million dots. 

We then taped them together.  It took quite a while, and was about 40 feet long when rolled out full length.  It is a most rewarding moment each year when we  unroll "THE MILLION" and let the students walk along it, imagining that each dot is a dollar bill.

We took this picture of our million dots to give you an idea of the magnitude of 1,000,000.

Copy of the million.jpg (14467 bytes)

Here is a closeup.  Each square you see here has 1,105 dots in it.

closeup of the million.jpg (14554 bytes)dots.gif (4513 bytes) So this is a picture of @ 40,000 dots.


Now find a friend or two and try these together.
Working together on this helps guarantee that you get the correct answers.  You can check each other and catch mistakes.)

Get yourself your calculator on the screen (click here if you need to learn how to get a calculator on your computer screen)

Use your calculator to answer these questions:

  1. How long is a million seconds in:





  2. How long is a million inches in:


  3. How many years is a million days?

  4. If a sheet of paper is .004 in thick, how
    many inches thick would one million sheets

    How many feet thick is this?
  5. If you make $5.25 per hour, how many hours
    would you have to work to earn your first

    How many 8 hour work days is this?

    How many 365 day years is this?
  6. A healthy person's heart will beat 65 times per minute.
    How long will it take to beat 1,000,000 times in:



  7. If you brush your teeth twice per day, every day of your
    life, will you brush a million times?

In the space below, make up 3 questions involving a
million of something and solve them. 












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