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    How much is a million, a billion, or a trillion?

    How much is a million, billion, trillion?
    Wise Young PhD MD
    The W. M. Keck Center for Collaborative Neuroscience
    Rutgers, the State University of New Jersey, Piscataway, NJ 08854-8087

    We often speak casually of millions, billions, or even trillions. We are accustomed to thinking of cities with millions of inhabitants, government agency budgets that add up to billions, and even the United States debt that that is now close to $9 trillion (Source). Most people don't appreciate these numbers.

    Let's start with a million.
    • A million minutes is nearly two years (1 year, 329 days, 10 hours and 40 minutes). Put in another way, it will take you nearly two years to spend a million dollars if you paid a dollar a minute.
    • A book called "How much is a million?" tried to explain the concept of a million to children, pointing out that it would take a person 23 days of non-stop counting to count a million anything, including dollars (Source).
    • If you walked a million steps, you can walk to Boston from New York (approximately 200 miles), assuming that each of your steps is a bit longer than a foot (a million feet is 189 miles).
    • Since each dollar bill weighs about a gram and each pound has about 454 grams, a million dollars in one dollar bills weighs about 2202.6 pounds (Source). In 20 dollar bills, a million dollars would still weigh 110 pounds. In 100 dollar bills, it would weigh 22.0 pounds.
    • A stack of 1000 bills is about a foot tall. Therefore, a million dollar stacked on top of each other would be 1000 feet tall. The Empire State Building is 1250 feet tall. A dollar bill is about 6 inches by 2.5 inches (15.7 cm by 6.6 cm) or about 0.10 square foot. So one cubic feet of $1 bills has about $10,000. A million dollars would take up about 100 cubic feet.

    A billion is of course 1000 million. You can multiply every thing above by 1000 but using $100 bills is a bit more practical.
    • A billion minutes ago is about the time of the birth of Christ.
    • A billion steps is more than 200,000 miles. The circumference of the earth is only 25,000 miles. Therefore, one can walk around the earth at least 9 times and possibly 10 times.
    • A billion dollars in $100 bills would weigh 22,000 pounds, over 1,100 cubic feet of bills.
    • A stack of $100 bills for a billion dollars would be 10,000 feet tall, taller than the tallest building in the United States and taller than any mountain east of the Rockies, including Mt. Washington (6288 ft, the tallest mountain in Northeast United States).
    • It would take 230 days to count the 10 million $100 bills. That is to count $1 billion.
    • On September 7, 2003, President Bush asked Congress to grant an additional $87 billion to continue the war in Iraq and Afghanistan. The $87 billion would cover a whole football field with $100 bills to the depth of 6 inches. By September 2007, the United States will have spent $315 billion on the war (Source). The Senate is working on adding another $50 billion. The $365 billion would fill a football field to a depth of 2 feet with $100 bills.
    • Filling a football field with $100 bills may seem sort of silly but it is not far from what the Bush Administration did. During Paul Bremer's tenure as administrator of Iraq, the United States shipped bales of cash to Iraq. The total amount cash sent was over $12 billion, requiring a football field size warehouse to store the cash. A special inspector general for the Iraqi reconstruction said that $8.8 billion is unaccounted for after being given to the Iraqi ministries. But more interesting, illustrating the physical dimensions of the cash shipped, $4 billion of the cash is missing, some 363 tons of it (Source).

    A trillion is an mind-boggling number, well beyond the capability of most of us to imagine. The following will illustrate.
    • A trillion minutes ago is 31,688 years ago, close to the beginning of human history (Source. In other words, if you spent a dollar per minute, you could barely spend a trillion dollars during all of known human history. Even if you spent $100 per minute, you would not be able to spend $1 trillion in 300 years, virtually the entire history of the United States.
    • Packed in bales of $100 bills (each weighing a gram), a trillion dollars would be 10 billion $100 bills, or about 10 million kilograms, 22 million pounds, or over 10,000 tons of cash (at 2000 pounds per ton). A trillion dollars in $100 bills would occupy a million cubic feet of space. It would fill a football field 6 feet deep. Before the end of 2008, the United States is likely to have spent over a trillion dollars on Iraq.
    • The United States now has a national deficit that will surpass $9 trillion by the end of 2007 and probably $10 trillion by the time President George W. Bush leaves office in 2008 if he is not impeached. Over a third of this deficit was added by the Bush Administration since 2001. In other words, the Bush Administration has spent more than 3 trillion dollars over the amount of taxes that it has collected in the past 6 years. This debt is being placed on the shoulders of our children.

    You know, a billion here and a billion there, all of a sudden we are talking about real money, money that is too much to count, too much to weigh, and too much to imagine.

    Wise.

    #2
    interesting stuff, wise.

    seems our lovely president can spend billions upon billions at the blink of an eye. he blows these statistics out of the water, hahaha.

    Comment


      #3
      I recently tried to imagine what 3 million people with spinal cord injury would look lik. That is approximately the number of people with spinal cord injury on earth. If we gather all of people with spinal cord injury in one place, the 3 million people would represent the third largest city in the United States (Source). As of July 1, 2005, New York had 8.14 million people, Los Angeles had 3.84 million, and Chicago had 2.84 million. But, people with spinal cord injury seldom live alone and if we include their families and caretakers, we are talking about a city that is bigger than any city in the United States.

      However, if we compare 3 million people with the populations of cities in china, the SCI city would be a relatively small city. Most Americans have little idea how big Chinese cities are. Probably none have heard of a city called Chongqing, located just south of the Three Gorges dam, in the province of Szechuan. I recently went to Chongqing and was stunned when somebody told me that it has 32 million people. I thought to myself that this must be the largest city in the world!

      I realize that there is no way that one can fit 32 million people into an area of land that can be legitimately called one city. Chongqing is formally classified as a "city district" that represent the city and all its suburbs. For comparison, the Beijing City District has 13 million in 2001 and currently probably has over 18 million people. The Shanghai City District had 16.4 million in 2001 and currently has over 18 million (url=http://www.citypopulation.de/China.html]source[/url]).

      In any case,
      • 3 million people in wheelchairs would occupy 300,000 square kilometers, if each took up a square meter of space. That is a 547 km by 547 km (328 x 328 miles) space.
      • 3 million people and their families using 1000 square feet of living space each would add up to more than 3 billion square feet. Any way that you look at this, it is a huge number.

      Wise.

      Comment


        #4
        Could the number of people affected with SCI be something like this; 3 million SCI’d with an average of one occupied from health care systems (doc, nurse PT, OT, assistants etc.) should give 6 million. Then if we compare to general traffic accidents I think the number affected by one accident is something like 4 or 5 (family members, relatives etc.). But let’s say 4. That would give 24 million. To take some population figures from here that would mean the total population of Denmark, Sweden, Finland, Norway and Iceland. That’s quite a few countries and people if looking at it like that? And why will not those countries help either?

        Comment


          #5
          Originally posted by Leif
          Could the number of people affected with SCI be something like this; 3 million SCI’d with an average of one occupied from health care systems (doc, nurse PT, OT, assistants etc.) should give 6 million. Then if we compare to general traffic accidents I think the number affected by one accident is something like 4 or 5 (family members, relatives etc.). But let’s say 4. That would give 24 million. To take some population figures from here that would mean the total population of Denmark, Sweden, Finland, Norway and Iceland. That’s quite a few countries and people if looking at it like that? And why will not those countries help either?
          Leif, absolutely.

          Three million people with spinal cord injury do not live by themselves. There are family members, caregivers, doctors, nurses, physical therapists, psychiatrists/psychologists, counselors, and social workers. We should consider the industry. In the United States, it is estimated that each person with spinal cord injury probably expend over $10,000 per year on catheters, tape, chucks, medications, wheelchairs, and other devices/supplies. That is a whole industry of people, estimated in the United States alone to cost over $10 billion per year.

          What I was trying to express was a bit more geeky, the fact that 3 million people in wheelchairs would occupy a space of 300,000 square kilometers! Could this be true? As I think about it, this cannot be. Let me go through the arithmetic again. One square kilometer is 1000 x 1000 meters or 1 million square meters. Therefore, if each person with a wheelchair occupied one square meter, 3 million people in wheelchairs would occupy 3 square kilometers not 300,000 square kilometers. I was wrong.

          Sigh.

          Wise.

          Comment


            #6
            President Bush was in a meeting about some recent bombings in Iraq. One of the Secretary of defense personnel told the President that three Brazilian people were killed in one of the bombings. The President dropped his head into his hands and stayed that way for several minutes. Everyone at the table was wondering what was the matter with the President. Finally, Bush lifted up his head and asked- that is horrible... How many is a brazillion?

            Comment


              #7
              The question of how big a billion is depends on which side of the Atlantic you learn your maths on:
              AMERICAN BRITISH
              1012 Trillion Billion
              1015 Quadrillion Thousand billion
              1018 Quintillion Trillion
              1021 Sextillion Thousand trillion
              1024 Septillion Quadrillion

              and so on

              To us a billion is a million million , and a trillion is a million billion.
              Last edited by Adrian; 23 Mar 2007, 5:31 PM.

              Comment


                #8
                Right, we use; million, milliard, billion, billiard, trillion and trilliard (increasing with three zeros in each step). Thus also the pool game billiard with 15 balls... We call a US billion (a million million) a milliard.
                Last edited by Leif; 23 Mar 2007, 5:41 PM.

                Comment


                  #9
                  Originally posted by Leif
                  Right, we use; million, milliard, billion, billiard, trillion and trilliard (increasing with three zeros in each step). Thus also the pool game billiard with 15 balls... We call a US billion (a million million) a milliard.
                  I have never heard of a US billion? A regular billion is a thousand million. A trillion is a million million. Wise.

                  Comment


                    #10
                    Originally posted by Wise Young
                    I have never heard of a US billion? A regular billion is a thousand million. A trillion is a million million. Wise.
                    There are no such thing like a US billion of course (you’re’ bankrupt), maybe a US gallon or an Imperial gallon sold to you at best?

                    But can you find out how shotgun barrels where named 12, 16 and 20 occurred? It is strange actually, given the times we live in, not if consider history though. No wonder that mm, inch and gauge play with us. Oh, the lazy Brit’s again.

                    Comment


                      #11
                      Leif & Adrian are correct, although Leif mistyped when he said (in parentheses) that a million million is a milliard.
                      As he says, a milliard is the same as a US billion, that is, a thousand million, 10^9. In most of the world, a billion is 10^12. Numbers are unambiguous, the names aren't. Find a comparison chart here.

                      When I was a child I learned that "a pint's a pound, the world around." But it's true only in the USA.
                      - Richard

                      Comment


                        #12
                        Originally posted by rfbdorf
                        Leif & Adrian are correct, although Leif mistyped when he said (in parentheses) that a million million is a milliard.
                        As he says, a milliard is the same as a US billion, that is, a thousand million, 10^9. In most of the world, a billion is 10^12. Numbers are unambiguous, the names aren't. Find a comparison chart here.

                        When I was a child I learned that "a pint's a pound, the world around." But it's true only in the USA.
                        - Richard
                        Wow, is that true? A billion in Europe is really a trillion? I found this very scholarly discussion of the subject

                        http://mathforum.org/library/drmath/view/52579.html

                        American vs. European Billion

                        Date: 07/30/2000 at 18:42:34
                        From: Walter
                        Subject: Difference between an American and a European billion

                        I don't know if this is really a math question but I asked myself
                        this question during my whole school time. Even my teachers can't
                        answer this question.

                        The American system is:
                        10^06 = million
                        10^09 = billion
                        10^12 = trillion
                        ...

                        The European system (formerly used in Britain, still used in Germany)
                        is:
                        10^06 = million
                        10^09 = thousand million
                        10^12 = billion
                        10^15 = thousand billion
                        10^18 = trillion
                        10^21 = thousand trillion
                        ...

                        Why the differences? I hope you can help me.

                        Walter

                        Date: 07/30/2000 at 19:08:07
                        From: Doctor Anthony
                        Subject: Re: Difference between an American and a European billion

                        The reason for the difference is historical and relates to the fact
                        that Latin is not taught to the same extent in America as in Europe.
                        The bi-million, tri-million is an obvious extension from 10^6 to 10^12
                        to 10^18 in the European system and these become billion and trillion,
                        respectively.

                        In America the need for a simple word for 1000 million and an absence
                        of Latin led to the misappropriation of the word 'billion'. England
                        held out for a long time with the 10^12 meaning of billion, but was
                        eventually overwhelmed by the sheer weight of scientific and
                        mathematical literature that used the American interpretation, so
                        billion in England is now used in the American sense. Europe may
                        eventually follow suit, but it will be a change from a logical system
                        to an arbitrary one.

                        - Doctor Anthony, The Math Forum
                        http://mathforum.org/dr.math/

                        Date: 04/10/2001 at 17:12:00
                        From: Doctor Peterson
                        Subject: Re: Difference between an American and a European billion

                        It sounds plausible, especially from a British perspective, that the
                        "arbitrary" American system should be due to our lack of education;
                        but I'm not sure the charge holds up to historical investigation. I'm
                        suspicious, in the first place, because I know from my own ancestors'
                        heritage that Latin was an important part of American education at
                        least in the 19th century, and surely also before then for those who
                        were educated. It may be true that Latin is not taught enough here,
                        but that has not always been true.

                        As our friend Jeff Miller says , first quoting D. E. Smith,

                        http://members.aol.com/jeff570/m.html

                        The French use of milliard, for 10^9, with billion as an
                        alternative, is relatively late. The word appears at least as
                        early as the beginning of the 16th century as the equivalent
                        both of 10^9 and of 10^12, the latter being the billion of
                        England today. By the 17th century, however, it was used in
                        Holland to mean 10^9, and no doubt it was about this time that
                        the usage began to change in France.

                        [This isn't quite clear, but "billion" meant 10^9 in France at least
                        by the early 18th century.]

                        As to the American usage, taking a billion to mean a thousand
                        million and running the subsequent names by thousands, it
                        should be said that this is due in part to French influence
                        after the Revolutionary War, although our earliest native
                        American arithmetic, the Greenwood book of 1729, gave the
                        billion as 10^9, the trillion as 10^12, and so on. Names
                        for large numbers were the fashion in early days, Pike's
                        well-known arithmetic (1788), for example, proceeding to
                        duodecillions before taking up addition.

                        Further, from the OED,

                        The name [billion] appears not to have been adopted in Eng.
                        before the end of the 17th c. .... Subsequently the application
                        of the word was changed by French arithmeticians, figures
                        being divided in numeration into groups of threes, instead of
                        sixes, so that F. billion, trillion, denoted not the second
                        and third powers of a million, but a thousand millions and a
                        thousand thousand millions. In the 19th century, the U.S.
                        adopted the French convention, but Britain retained the
                        original and etymological use (to which France reverted in 1948).
                        Since 1951 the U.S. value, a thousand millions, has been
                        increasingly used in Britain, especially in technical writing
                        and, more recently, in journalism; but the older sense "a
                        million millions" is still common.

                        Putting this together, we see that the "American" use of "billion"
                        originated not here but in France; and that it was probably based not
                        on stupidity, but on practicality (another well-known characteristic
                        of Americans), as there was more need for a name for 10^9 than for
                        10^12. There _is_ logic behind the usage; in this system, billion
                        doesn't mean "million squared" but "second -illion" counting by
                        thousands. It's hardly different from deciding whether to index
                        arrays starting at 0 or 1. You just have to choose where to start and
                        how big a step to take, and the numbers follow a logical progression.

                        I fully agree that the original British usage is nicer and easier to
                        explain, and I wish it were the standard system; but the other is not
                        really arbitrary. It should also be noted that France, not Britain,
                        was the center of mathematical scholarship at the time "billion" was
                        imported into America, so it can be reasonably suggested that the
                        Americans adopted it for the same reason the British have more
                        recently: it was used by the most important writers.

                        -Doctor Peterson
                        http://mathforum.org/dr.math/
                        Chinese think in 10,000 units or wan4. So, for example, a thousand is qian1 (1,000), ten thousand (10,000) is wan4, and one hundred million (100,000,000) or ten thousand ten thousands is yi4. Thus, a billion would be ten yi4. See http://www.mandarintools.com/numbers.html

                        Amazingly, the ancient Chinese had names for very large numbers, i.e. zhao for a trillion (10^12), jing for 10^16, gai for 10^20, zi for 10^24, rang for 10^28, gou for 10^32, jian for 10^36, zheng for 10^40, zai for 10^44, and ji for 10^48, henghesha for 10^52, unpronounciable for 10^56, nayouta for 10^60, bukesiyi for 10^64, wulian for 10^68, and dashu for 10^72. http://en.wikipedia.org/wiki/Chinese_numerals

                        Wise.
                        Last edited by Wise Young; 29 Mar 2007, 7:15 AM.

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