Download If I were to count….

If I were to count to a million, how
long would it take?
By Vincent Sapone
Introduction
• People routinely come across large
numbers they do not fully understand.
• Nothing can fully alleviate the conceptual
difficulties involved in understanding vastly
gigantic numbers.
• Despite this, it will give us a sense of scale
to consider how long it might take a
person to count to a million or a billion and
beyond…
The Question:
• How long would it take to count to a
million?
• Think about it and take a guess before
going to the next slide.
Methodology
• How long it would take can be determined
very easy mathematically.
• There are a million numbers between one
and one million so we can roughly assume
each one will take about 2 seconds to say.
Method 2
• It might be easy to say “One, two, three,
four” and so on but it takes a lot longer to
count a higher sequence such as:
• 445,226 … 445,227 ….445,228…
• So two seconds per number seems fair.
As you count higher and higher larger time
intervals will be needed.
• This study starts using the “two second
rule” but as you pass the billion mark, it
must be maintained that two seconds is no
longer a feasible time. For example…
• The number 1,300,400,668 is
• One billion, three hundred million, four
hundred thousand, six hundred and sixty
eight…
• Therefore the two second rule seems
insufficient.
How Long would it take?
• Now that the method is cleared up, how
long would it take to count to a million?
One Million
• To count to a million without stopping for
anything would take about 23 days.
Calculation
• 1 million numbers at 2 seconds per
number is 2 million seconds.
• There are 86,400 seconds in a day
(60x60x24).
• 2,000,000 / 86,400 = 23.1 days.
A Billion
• The time required to count to a million
usually impresses some people.
• Now we want to know how long it would
take to count to one billion?
• What do you think?
Calculation
• The three second rule applies.
• Three seconds per number (1 billion
numbers) = 3 billion seconds.
• That number divided by 86,400 yields the
total number of days.
• Surprisingly, the figure is so high we have
to divide it by 365 to convert it into years.
A Billion
• In order to count to one billion assuming a
three second rule, it would take about 95
years.
Billion
• That 95 years is without time to eat, drink,
sleep or use the bathroom.
• Therefore, it is safe to say that no human
could ever count to a billion.
A trillion
• If we upped the number to a trillion, how
long would it take to count to it?
Method
• The two or even three second rule
probably is far too generous now. These
strings of numbers would take a bit longer
to say…
• 558,456,345,346,663…
• 558,456,345,346,664…
A Trillion
• Assuming the two second rule, it would
take about 63,000 years.
• Using a (more likely) three second rule it
would take 95,000 years
• Four seconds might be even more like it.
6 Trillion
• To count to six trillion, it would take about
570,000 years with the three second
method.
•
Six Trillion miles is the distance light travels in one year.
Application
• Thus, if we said the earth is 93 million
miles away from the sun or the nearest
star to the earth is over 25 trillion miles
away, can we really “fathom” how far
these distances are from us?
Probably not.
• We just know that they are really far and
can understand them only in comparison
to other distances.
• Yet these stellar distances that were just
mentioned are actually baby steps on
astronomical scales…
• HAPPY COUNTING!!!
•
For a great Children’s Book, check out “How Much is a Million?” It does
what this power point did only it has lots of pictures and some other
questions such as how big of a fish tank would you need to fit a billion
goldfish in?”.