After How Much Is a Million?, my book about big numbers, appeared in 1985, I quickly discovered what everyone really wanted to know: “How much is a million dollars?” It gave me the idea for my second book, If You Made a Million. Now everyone is thinking about the federal bailout of 700 billion dollars, aka $700,000,000,000 – with an extra 30 billion thrown in, or not, for good measure. So, how much is 700 billion dollars?
Let’s start by counting the way the characters count in On Beyond a Million (yet another book I wrote with “million” in the title). In that book, the characters count not by ones the whole way (or they’d never get beyond a million) but by ones to ten, by tens to a hundred, by hundreds to a thousand, and so on. Mathematicians would say they are counting by “powers of ten,” but in the book I call it “Power Counting.” Let’s just quickly “power-count” our way from one to one mil
lion:
1 (one)
Did you notice that one million is three steps of power-counting past one thousand? Each step multiplies by 10, so one million is three of those, or 10 X 10 X 10, or one thousand times bigger than one thousand. One million is one thousand thousand. Let’s go on:
10,000,000 (ten million)
100,000,000 (one hundred million)
1,000,000,000 (one billion)
One billion is three steps past one million, or one thousand times one million. Just as one million is a thousand thousand, one billion is a thousand million. (In some countries, including Great Britain, they call it “one thousand million” instead of a “billion.”) Let’s do one more round:
10,000,000,000 (ten billion)
100,000,000,000 (one hundred billion)
1,000,000,000,000 (one trillion)
One trillion is one thousand billion. Did you notice one hundred billion in bold? We’re going back to it. Take seven of those and what have you got? Seven hundred billion. In dollars, it’s the bail-out. One heck of a lot of money. Oh, we could figure out how high 700 billion kids or 700 billion one-dollar bills would stack if we were inclined to stack them, or how many homes it could build or heat, and so forth. . . but let’s not. Instead, let’s try to understand the magnitude of this giant pot of cash by taking a step back from big money to very small money: one cent.
Would you rather have a penny that gets doubled every day for a month (let’s say a 30 day month)… or would you rather have a million dollars in cash today, but not another cent for the rest of the month? Maybe you’ve heard this one before but no matter. I’ve told it dozens of times, and it still amazes me that doubling the pennies gives a pay-off of over $5 million in pennies on the 30th day (not to mention all the pennies accumulated from the other days)! Don’t just believe me -- do the math. It’s not hard, especially if you round off along the way.
So, when you put one cent through 29 rounds of doubling it gets really big, really fast. That’s the power of doubling. (There have been some fine picture books based on this mathematical principle, including One Grain of Rice and The King’s Chessboard.) But what happens every step of the way when we put a zero after a number, when we “power count”? We aren’t doubling; we’re multiplying by ten. I don’t know of any verb for that, so I have invented one: decktuple. (Please use it widely.) If you thought doubling was powerful, think of decktupling – power to the max!
My favorite way to see the difference between big numbers and appreciate their magnitude is to think of seconds. One million seconds is about eleven and a half days. One billion seconds is -- take a guess before you read on – about 32 years. And one trillion seconds is about 32,000 years. So the difference between a million, a billion and a trillion is like the difference between 11.5 days, 32 years and 32,000 years! I like to say that I have a pretty good idea of what I’ll be doing a million seconds from now. . . I have no idea of what I’ll be doing a billion seconds from now. . . but I have an excellent idea of what I will be doing a trillion seconds from now.
And what about 700 billion? That’s seven-tenths, or 70%, of the way to a trillion. In seconds it would be 22,400 years. I am writing this on December 28, 2008 at about 9pm. If instead of dollars we talked about seconds and I started clocking them right now, I would get to a million on Jan. 9th at about 9am . . . I would get to a billion early in the year 2040 . . . and I (or someone, I hope) would get to 700 billion in the year 24000 (not 2400 but 24000!), give or take a few hundred years.
Does this help explain the size of the bailout. Or does it just boggle your mind? Both are good.
lion:1 (one)
10 (ten)
100 (one hundred)
1,000 (one thousand)
10,000 (ten thousand)
100,000 (one hundred thousand)
100 (one hundred)
1,000 (one thousand)
10,000 (ten thousand)
100,000 (one hundred thousand)
1,000,000 (one million)
Did you notice that one million is three steps of power-counting past one thousand? Each step multiplies by 10, so one million is three of those, or 10 X 10 X 10, or one thousand times bigger than one thousand. One million is one thousand thousand. Let’s go on:
10,000,000 (ten million)
100,000,000 (one hundred million)
1,000,000,000 (one billion)
One billion is three steps past one million, or one thousand times one million. Just as one million is a thousand thousand, one billion is a thousand million. (In some countries, including Great Britain, they call it “one thousand million” instead of a “billion.”) Let’s do one more round:
10,000,000,000 (ten billion)
100,000,000,000 (one hundred billion)
1,000,000,000,000 (one trillion)
One trillion is one thousand billion. Did you notice one hundred billion in bold? We’re going back to it. Take seven of those and what have you got? Seven hundred billion. In dollars, it’s the bail-out. One heck of a lot of money. Oh, we could figure out how high 700 billion kids or 700 billion one-dollar bills would stack if we were inclined to stack them, or how many homes it could build or heat, and so forth. . . but let’s not. Instead, let’s try to understand the magnitude of this giant pot of cash by taking a step back from big money to very small money: one cent.
Would you rather have a penny that gets doubled every day for a month (let’s say a 30 day month)… or would you rather have a million dollars in cash today, but not another cent for the rest of the month? Maybe you’ve heard this one before but no matter. I’ve told it dozens of times, and it still amazes me that doubling the pennies gives a pay-off of over $5 million in pennies on the 30th day (not to mention all the pennies accumulated from the other days)! Don’t just believe me -- do the math. It’s not hard, especially if you round off along the way.
So, when you put one cent through 29 rounds of doubling it gets really big, really fast. That’s the power of doubling. (There have been some fine picture books based on this mathematical principle, including One Grain of Rice and The King’s Chessboard.) But what happens every step of the way when we put a zero after a number, when we “power count”? We aren’t doubling; we’re multiplying by ten. I don’t know of any verb for that, so I have invented one: decktuple. (Please use it widely.) If you thought doubling was powerful, think of decktupling – power to the max!
My favorite way to see the difference between big numbers and appreciate their magnitude is to think of seconds. One million seconds is about eleven and a half days. One billion seconds is -- take a guess before you read on – about 32 years. And one trillion seconds is about 32,000 years. So the difference between a million, a billion and a trillion is like the difference between 11.5 days, 32 years and 32,000 years! I like to say that I have a pretty good idea of what I’ll be doing a million seconds from now. . . I have no idea of what I’ll be doing a billion seconds from now. . . but I have an excellent idea of what I will be doing a trillion seconds from now.
And what about 700 billion? That’s seven-tenths, or 70%, of the way to a trillion. In seconds it would be 22,400 years. I am writing this on December 28, 2008 at about 9pm. If instead of dollars we talked about seconds and I started clocking them right now, I would get to a million on Jan. 9th at about 9am . . . I would get to a billion early in the year 2040 . . . and I (or someone, I hope) would get to 700 billion in the year 24000 (not 2400 but 24000!), give or take a few hundred years.
Does this help explain the size of the bailout. Or does it just boggle your mind? Both are good.
5 comments:
It helped and it boggled, both!
Thanks for this excellent explanation, David.
I've requested "If You Made a Million" from the library to feature as a review on my blog in the coming weeks as part of National Financial Awareness month. It looks like a great book!
I've read If you Made a Million and it was VERY interesting. I find children's non-fiction very fun to read. I learn so much and it's just the basics, not all that extra stuff. Then if I want to know more I can look up adult nonfiction of the subject.
I read the book How Much is a Million, and it's a very good book.
The approach to numbers and
counting is brilliant.I'm interested of reading the second book: If You Made a Million.The explanation is very good indeed.I love the analogy of the money to times in second, it causes me look at it in a different perspective. I also find very interesting taking a step back from big money to very small money: one cent. It makes me appreciate the cent/penny and preventive me to despise their
value.
It boggles. Really. 2400 is too far in the future to really imagine, but 24,000 boggles me completely. What's that? 12 times longer than the time when JC was walking around Bethlehem?
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