How do you explain one million?
March 14, 2012 5:04 AM   Subscribe

Have you ever had "one million" (or one billion) explained in a satisfactory manner?

According to They Might Be Giants (who would never lie to me), if the sun were hollow, a million earths could fit inside (and it's only a medium-sized star)! Also, my 8th grade Civics teacher told us if a person counted eight hours per day, forty hours per week, it would take 150 years to count to one million. Do you know any other interesting/humorous/easy-to-grasp explanations of a million?

How about one billion? I recall something about a piece a paper where the number one up to the number one million would be basically all on one edge of the paper, and one billion would be on the opposite edge. AskMe, can you help me grasp giant number concepts? This previous question was interesting, but different.
posted by Glinn to Science & Nature (37 answers total) 9 users marked this as a favorite
A million is a square one thousand per side.

A billion is a cube one thousand per side.
posted by pompomtom at 5:18 AM on March 14, 2012 [3 favorites]

This article does a good job of visualizing what a million, billion, and trillion dollars looks like in cash (stacks of hundred dollar bills).
posted by windbox at 5:19 AM on March 14, 2012 [3 favorites]

Your civics teacher was way off. Supposing you could count one number per second, if you did it 24 hours a day, you'd be done in 12 days. So it would take you maybe four times longer if you were just counting forty hours a week -- so you'd still be finished in a matter of weeks.
posted by jayder at 5:28 AM on March 14, 2012 [7 favorites]

A full bathtub contains about 50 gallons of water, which is about 0.2 cubic meters, or 200,000 millileters. A teaspoon is a about 5ml. So it takes about 40,000 teaspoons of water to fill a bath.

Imagine having to fill 25 bathtubs with water using only a teaspoon. That's a million right there.

To visualize a billion, imagine having to fill 25,000 bathtubs with water. That's a bath for everyone in a medium sized town.
posted by unSane at 5:28 AM on March 14, 2012 [4 favorites]

Also, if you started in NYC and took a million steps in a straight line, you might end up in Seattle.
posted by unSane at 5:31 AM on March 14, 2012

There is a children's book called How Much is a Million? that does a pretty good job
posted by thewestinggame at 5:32 AM on March 14, 2012 [3 favorites]

a half teaspoon of water is 1-part-per-billion of an olympic swimming pool
posted by Flood at 5:39 AM on March 14, 2012

I am going to assume that your civics teacher was talking about a billion, because it's pretty close.

The average lifespan of a mammal is about a billion heartbeats. For humans it's about twice that.
posted by Nothing at 5:40 AM on March 14, 2012 [1 favorite]

Supposing you could count one number per second,

Counting is definitely slower than O(n) - probably something like O(n logn), as the number of digits is the critical factor for time per number.
posted by Dr Dracator at 5:55 AM on March 14, 2012 [1 favorite]

There have been (quite a lot) less than a million days since Jesus of Nazareth was born.
posted by caek at 5:59 AM on March 14, 2012

Also, if you started in NYC and took a million steps in a straight line, you might end up in Seattle.

Unless I'm doing the math wrong, this isn't true at all. Even if each footstep took you forward a whole yard, 3,000,000 feet west wouldn't even get you to the far side of Ohio.
posted by Rhaomi at 6:06 AM on March 14, 2012

you should read 'a short history of nearly everything' by Bill Bryson. He describes the science of our universe in laymans terms, great book. I couldn't find a quote on exactly one billion but here's another (long) take on numbers and time from the book:

“If you imagine the 4,500-bilion-odd years of Earth's history compressed into a normal earthly day, then life begins very early, about 4 A.M., with the rise of the first simple, single-celled organisms, but then advances no further for the next sixteen hours. Not until almost 8:30 in the evening, with the day five-sixths over, has Earth anything to show the universe but a restless skin of microbes. Then, finally, the first sea plants appear, followed twenty minutes later by the first jellyfish and the enigmatic Ediacaran fauna first seen by Reginald Sprigg in Australia. At 9:04 P.M. trilobites swim onto the scene, followed more or less immediately by the shapely creatures of the Burgess Shale. Just before 10 P.M. plants begin to pop up on the land. Soon after, with less than two hours left in the day, the first land creatures follow.

Thanks to ten minutes or so of balmy weather, by 10:24 the Earth is covered in the great carboniferous forests whose residues give us all our coal, and the first winged insects are evident. Dinosaurs plod onto the scene just before 11 P.M. and hold sway for about three-quarters of an hour. At twenty-one minutes to midnight they vanish and the age of mammals begins. Humans emerge one minute and seventeen seconds before midnight. The whole of our recorded history, on this scale, would be no more than a few seconds, a single human lifetime barely an instant. Throughout this greatly speeded-up day continents slide about and bang together at a clip that seems positively reckless. Mountains rise and melt away, ocean basins come and go, ice sheets advance and withdraw. And throughout the whole, about three times every minute, somewhere on the planet there is a flash-bulb pop of light marking the impact of a Manson-sized meteor or one even larger. It's a wonder that anything at all can survive in such a pummeled and unsettled environment. In fact, not many things do for long.”

Another funny one:

"of course, it is possible that alien beings travel billions of miles to amuse themselves by planting crop circles in Wiltshire or frightening the daylights out of some poor guy in a pickup truck on a lonely road in Arizona (they must have teenagers, after all), but it does seem unlikely"
posted by Under the Sea at 6:07 AM on March 14, 2012 [3 favorites]

Also, if you started in NYC and took a million steps in a straight line, you might end up in Seattle.

If every step is 3 feet, taking 1 million steps would get you 3 million feet. 3 million feet in miles is 568 miles. The distance between NYC and Seattle is roughly 2,800 miles. So it would take almost 5 million steps to get there.
posted by Cygnet at 6:08 AM on March 14, 2012

Under the Sea, I think you may have a typo. The age of the Earth is 4.5 billion years, not 4,500 billion years.
posted by Cygnet at 6:25 AM on March 14, 2012

Look up a few $5 million homes on luxury real estate websites. With a billion dollars you could buy two hundred of those! Of course, then you'd need another billion to cover taxes, etc.
posted by Fred Mars at 6:35 AM on March 14, 2012

Imagine 1 apple. Picture it in your mind.

Now imagine 10. Just another zero right?

How about 100? Doable.

1,000? Fathomable for some, possibly you as well.

10,000? Most cannot picture this accurately.

100,000 apples? All counted for? Nope. Humans cannot imagine this...

How much weight can you move?

1,000,000 one-dollar bills weighs 2,200lbs.
The world's heaviest squat completed by man is only half that.

Each zero added starts to exit the realm of fathomable.

93,000,000 miles on avg. from the Earth to the Sun.
8 minutes for light to reach us.

7,500,000,000 miles in diameter, of our solar system.
5 hours for light to travel the radius...out of our solar system.

Years before it hits the nearest star system.

100 Millenia for light to traverse our galaxy.

Over a million light years (how far light can travel in a year) to reach nearby major galaxies.

We can see 45 billion light years in any given direction, of our observable universe. Light from beyond this point has not and will not reach us, simply because at the edge of what we can see is the beginning of our universe. We can watch it develop, but ever so slowly.

Our universe, at minimum, contains 36,000,000,000,000,000,000,000,000,000,000,000.
We have recently come to think that our universe holds more planets than stars.

This is just the observable universe, mind you.

Back to the apples.... how far did you get again?
posted by JamesBlakeAV at 6:37 AM on March 14, 2012

Nobody has an intuitive grasp of big numbers. People who think they do are just fooling themselves. So don't bother. Keep working with small numbers, arranged like so:

Hundred: 102 (hecto)
Thousand: 103 (kilo)
Million: 106 (mega)
Billion: 109 (giga)
Trillion: 1012 (tera)

Those you can develop an intuitive feel for, and as long as you also spend a little time practicing multiplying powers of ten by adding the powers, you won't go too far wrong.

The people who try to do it all with raw intuition are the ones who end up worrying about things like this, because it really doesn't take much bigness to saturate our intuitive idea of it.
posted by flabdablet at 6:43 AM on March 14, 2012

Cheaper by the Dozen is a biography of the family of Frank Gilbreth and Lillian Moller Gilbreth, and their twelve children. The Gilbreths were pioneering experts in the fields of time and motion study and industrial efficiency.

At one point in the biography, Frank Gilbreth realised that his children were going to hear more and more often about "millions" of things. To show them what a million is, he took a large sheet of paper and drew a square, marked off a thousand equal subdivisions on each side, and then drew parallel lines in both directions, dividing the big square into 1,000 x 1,000 = 1,000,000 tiny squares. He then hung the paper on the wall, like a poster. A billion would be a thousand of those posters.

I want to do that myself.
posted by Multicellular Exothermic at 6:48 AM on March 14, 2012

To show them what a million is, he took a large sheet of paper and drew a square, marked off a thousand equal subdivisions on each side, and then drew parallel lines in both directions, dividing the big square into 1,000 x 1,000 = 1,000,000 tiny squares. He then hung the paper on the wall, like a poster.

Years ago, as a kid, I saw a poster like this at the Ann Arbor Children's Museum. It made a big impression on me at the time. I have no idea if it's still there, though.
posted by Johnny Assay at 7:05 AM on March 14, 2012

Bill Bryson’s calculation of a Trillion in Notes from a Big Country:

"Imagine, if you will, you are in a colossal safe in which there is $1 Trillion in clean crisp dollar bills. Imagine further that someone tells you you can keep each dollar bill you sign and you manage to sign one dollar bill every second. How long do you think it will take you to sign each and every dollar bill in that safe? A few weeks? A year?

Allow me to explain.

Signing one dollar bill each second will make you $1000 richer after 17 minutes. After 12 full days of furious dollar bill signing without any interruption, you will be a millionaire. That obviously means you will have $10 million after 120 days and $100 million after 1200 days (just over 3 full years of dollar bill signing). Here’s the great part. You will have signed enough dollar bills after 31,7 years to call yourself a billionaire and after almost 1000 years you will have signed enough dollar bills to be in Bill Gates’ league. Fact of the matter is, only after 31 709,8 years, without any interruption, will you have signed enough dollar bills to own the trillion dollars in the safe.
posted by peagood at 7:18 AM on March 14, 2012 [2 favorites]

JamesBlakeAV has hurt my head.
But seriously, thanks to everyone.
posted by Glinn at 7:28 AM on March 14, 2012

Helpful big number reference and orientation points:

Age of observable universe: 14 × 109 years
Age of Earth: 4.5 × 109 years

After finding a bunch of those that interest you and that you can remember, use proportionality to prime your intuition about related things.


Speed of light: 300 × 106 metres per second
Speed of electric signal in wire: about 2/3 of lightspeed, so 200 × 106 metres per second
Number of times the clock in a modern CPU ticks per second: 3.3 × 109
Distance a signal can travel in one CPU clock period: 200 × 106 metres per second ÷ 3.3 x 109 ticks per second = (200 ÷ 3.3) × 106-9 metres per tick = 60 millimetres per tick


Distance to Sun: 150 × 106 kilometres = 150 × 109 metres
Time taken for sunlight to reach Earth: 150 × 109 metres ÷ 300 × 106 metres per second = (150 ÷ 300) × 109-6 seconds = 0.5 × 103 seconds = 500 seconds = 8m20s

Distance light travels in one year: 300 × 106 metres per second × 86400 seconds per day × 365 days per year = 9.5 × 1015 metres = 9.5 trillion kilometres
Distance to nearest star (Proxima Centauri): 4.2 light years = 40 trillion kilometres

Distance to "next-door neighbor" Earth-like planet: 22 light years = 210 trillion kilometres

Speed of fastest rocket ever deployed: 15 kilometres per second

Travel time to "next-door neighbor" at that speed: 210 trillion kilometres ÷ 15 kilometres per second = (210 ÷ 15) trillion seconds = 14 trillion seconds = 444 thousand years (we won't be borrowing a cup of sugar any time soon).
posted by flabdablet at 7:34 AM on March 14, 2012

Population of earth as pixels (as of June 2006, ~6.5 billion people). Via the Wayback Machine since the original page seems to be gone.
posted by DevilsAdvocate at 7:44 AM on March 14, 2012

A thousand seconds is 16 minutes, 40 seconds.
A million seconds is 11 days, 13 hours, 46 minutes, 40 seconds.
A billion seconds is 31 years, 251 days, 15 hours, 13 minutes, 4 seconds.
A trillion seconds is more than 31,000 years.
posted by Chocolate Pickle at 7:48 AM on March 14, 2012 [1 favorite]

Have you seen the Powers of Ten book or video? The book is out of print, but the video must be on YouTube somewhere.
posted by Flannery Culp at 7:58 AM on March 14, 2012

One Millon is Big, one Billion is Bigger, featuring the Fat Boys.

"One thousand times one million, that's one billion!"
posted by Wild_Eep at 8:45 AM on March 14, 2012

"One million isn't even 1 percent of one billion."
posted by Wild_Eep at 8:46 AM on March 14, 2012

On the other hand, if you placed one dollar first square of a chessboard, two on the next, four on the next, eight on the next, and so on, doubling as you went, at the end of the first row you would have $128.

At the end of the second row, $32,769

You'd have more than $1,000,000 piled on the 3rd square of the third row (#19)

You'd have more than $1 billion piled on the fifth square of the fourth row (#29)

You'd have more than $1 trillion piled on the 7th square of the fifth row (#39)

You'd have more than the annual GDP of the US piled on the third square of the sixth row (#43)

On the final square you'd have more than $9,000,000,000,000,000,000 ($9 quintillion)
posted by unSane at 8:48 AM on March 14, 2012 [1 favorite]

*32768 on the end of the second row, obviously
posted by unSane at 8:49 AM on March 14, 2012 [1 favorite]

I have always liked The MegaPenny Project for visualizing large numbers. Also, remember that a million and a billion do not mean the same thing to everyone.
posted by TedW at 9:08 AM on March 14, 2012

This XKCD graphic is relevant.
posted by jsturgill at 9:33 AM on March 14, 2012

I've got a thing for money vs. volume thanks to my occasional coin accumulations, and I enjoyed the heck out of Rob Cockerham's "[How Much Is Inside] A Million Dollars?" You'll cherish this next time you watch a TV show where someone hands someone else a slim briefcase said to contain $7 million, or the like.

Also, I once read the claim that Jesus walked the Earth a billion minutes ago, which was closer to being true at the start of the 20th century-- a billion minutes is just over 1902 years.

Oh, and for those of us still enjoying the imperial system of measure, the speed of light is 186,000 miles/second, or about 12 million miles/minute.
posted by Sunburnt at 9:54 AM on March 14, 2012

Astronomy Picture of the Day did this a couple of days ago.
posted by Chocolate Pickle at 10:12 AM on March 14, 2012


Notch changed the algorithm.
posted by JamesBlakeAV at 1:44 PM on March 14, 2012

With money, I have found it helpful to imagine getting 10 crisp $100 bills at the ATM and standing them up on edge in a neat litttle stack or row that is let's say1 millimeter thick. So 1 mm = $1,000. Now you use the metric system to multiply into millions and billions. One million dollars = one thousand thousand dollars = a tight horizontal row of bills one kilometer long. Use a map to pick out a familiar point 1,000 km away from you to visualize a billion. It does get harder to conceptualize at a trillion.
posted by newmoistness at 2:24 PM on March 14, 2012

Arggh, sorry! Of course I screwed that up completely. If a thousand dollars = i mllimeter, then a thousand thousand dollars = 1 million dollars = 1 METER, then a billion = 1 kilometer, then a trillion = one thousand kilometers. It gets harder AFTER a trillion.

(slinks off innumerately)
posted by newmoistness at 2:29 PM on March 14, 2012

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