When I was a kid, a "millionaire" was a very wealthy person: someone who was set for life. In The Beverly Hillbillies, the popular TV comedy of the 1960s and 1970s, crude oil "made Jed a millionaire". Today, retiring on a million dollars takes strategy. Even the definition of millionaire is shifting to describe a person who earns a million dollars a year.
The definition of a billion and a trillion
Growing up in Canada, I went to French immersion school. I took math in French, where I learned the words milliard and billion: in English, 'billion' and 'trillion' respectively. Ever since, I've been unclear about what a billion is: is it a thousand times a million, or a million times a million?
As it turns out there are two definitions of a billion: a 'short scale' definition (a thousand times a million) and a 'long scale' (a million times a million). The short scale is now commonly adopted as an international standard, but as lexicographer Susie Dent explained for the BBC, there's a persistent generational and cultural divide between the two.
Under the short scale standard: One million is 1,000,000. One billion in 1,000,000,000, One trillion is 1,000,000,000,000.
Making big numbers make sense
But how can we understand what big numbers like these really mean? Here are two strategies to help you relate to big numbers.
Pin big numbers to everyday concepts
One way of making sense of big numbers is to pin them to concepts, like time and distance, that we use in our everyday life:
16 miles is a distance you could cover in 5 and a half hours, walking at a moderate pace. 15,782 miles is just about 3/4 of the way around planet earth. A trillion inches, by contrast, is about 633 times around the planet.
Rescale big numbers to the level of your life
You can also shrink big numbers down to a level that makes sense in your life. Here's an example:
Imagine you earn $50,000 a year and your friend is one of those new millionaires, earning $1,000,000 annually. Her salary is 20 times bigger than yours, so to your millionaire friend, things cost 20 times less. A decent bottle of wine in the $12 and under section costs her 60 cents. A $40 dinner out at a restaurant costs her $2. Her $10,000 monthly rent is your $500 rent.
As my friend Scott said, "It's like dog years."
Big numbers and social justice
If we can't understand what big numbers mean, it's hard to engage with news about issues like climate change, national economies, population growth, and the redistribution of wealth. Big numbers sound big. The issues they describe sound scary. And it's hard to stay in a scary space without understanding what's there.
I suspect that for many of us this mixture of fear, confusion and guilt leads to passivity. We let the words "billion" and "trillion" wash over us without stopping to ask what they really mean. We feel defeated before we've even begun to inquire. Numeracy is a simple and powerful tool to fight this kind of defeat.
A million is 106, or 1,000,000. A billion is one thousand million, or 1,000,000,000 (109). This is the common usage in English-speaking countries and is called the short scale. Countries in continental Europe and Latin America use the long scale where a billion is a million millions (1012).
The word billion originated from French word bi- (“two”) + -illion; i.e. a million million. It was first coined by Jehan Adam in 1475 as by-million and then rendered as byllion by Nicolas Chuquet in 1484.
Million originated from the Italian milione, from the Latin mille + the augmentative suffix -one.
| 10 to the 9th power (10^9) | 10 to the 6th power (10^6) |
| 1,000,000,000 | 1,000,000 |
The magnitude of difference between billion and million can be illustrated with this example of the time scale:
- A million seconds is 12 days.
- A billion seconds is 31 years.
- A trillion seconds is 31,688 years.
The video further compares the three numbers
Other large numbers
- Million=1,000,000
- Billion=1,000,000,000
- Trillion=1,000,000,000,000
- Quintillion=1,000,000,000,000,000,000
- Sextillion=1,000,000,000,000,000,000,000,000.
- Nonillion=1,000,000,000,000,000,000,000,000,000,000
- CENTILLION=1 followed by 303 zeros
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Gross vs Net
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Income vs Revenue
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Itemized vs Standard Deduction
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The Piraha tribe is a group living in the jungles of South America. They are well known because they do not have a way to count past two. According to Daniel L. Everett, a linguist and professor who spent decades living among and studying the tribe, the Piraha have no number words to distinguish between these two numbers. Anything more than two is a “big” number.
Most people are similar to the Piraha tribe. We may be able to count past two, but there comes a point where we lose our grasp of numbers. When the numbers get big enough, intuition is gone and all we can say is that a number is "really big." In English, the words "million" and "billion" differ by only one letter, yet that letter means that one of the words signifies something that is a thousand times larger than the other.
Do we really know how big these numbers are? The trick to thinking about large numbers is to relate them to something that is meaningful. How big is a trillion? Unless we’ve thought of some concrete ways to picture this number in relation to a billion, all that we can say is, "A billion is big and a trillion is even bigger."
First consider a million:
- One million is a thousand thousands.
- One million is a 1 with six zeros after it, denoted by 1,000,000.
- One million seconds is about 11 and a half days.
- One million pennies stacked on top of each other would make a tower nearly a mile high.
- If you earn $45,000 a year, it would take 22 years to amass a fortune of 1 million dollars.
- One million ants would weigh a little over 6 pounds.
- One million dollars divided evenly among the U.S. population would mean everyone in the United States would receive about one-third of one cent.
Next up is one billion:
- One billion is a thousand millions.
- One billion is a 1 with nine zeros after it, denoted by 1,000,000,000.
- One billion seconds is about 32 years.
- One billion pennies stacked on top of each other would make a tower almost 870 miles high.
- If you earn $45,000 a year, it would take 22,000 years to amass a fortune of one billion dollars.
- One billion ants would weight over 3 tons—a little less than the weight of an elephant.
- One billion dollars divided equally among the U.S. population would mean that everyone in the United States would receive about $3.33.
After this is a trillion:
- One trillion is a thousand billions, or equivalently a million millions.
- It is a 1 with 12 zeros after it, denoted by 1,000,000,000,000.
- One trillion seconds is 32,000 years.
- One trillion pennies stacked on top of each other would make a tower about 870,000 miles high—the same distance obtained by going to the moon, back to Earth, then to the moon again.
- One trillion ants would weigh over 3,000 tons.
- One trillion dollars divided evenly among the U.S. population would mean that everyone in the United States would receive a little over $3,000.
Numbers higher than a trillion are not talked about as frequently, but there are names for these numbers. More important than the names is knowing how to think about large numbers. To be a well-informed member of society, we really should be able to know how big numbers like a billion and trillion really are.
It helps to make this identification personal. Have fun coming up with your own concrete ways to talk about the magnitude of these numbers.