If I were to count to a million, how long would it take? By Vincent Sapone.

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?”.