What's the difference between a million, a billion and a trillion?
Over the past few decades, big numbers have become normalized in our conversation. We hear about billions and trillions in the news every day:
- With a net worth of 75 billion, Bill Gates is the richest person in the world.
- The Unites States' wars in Iraq and Afghanistan cost its taxpayers $1.6 trillion.
- Insurance losses from the Fort McMurray wildfires this spring could top $9 billion.
But what do these words really mean? If you're anything like me, you can wrap your head around the idea a million, but you're hazy about billions and trillions. These big numbers just sound big. And the issues they describe sound scary.
Without a way to understand big numbers, it's difficult to engage in the issues they describe.
What we're experiencing is a symptom of a kind of linguistic inflation. Numbers are getting bigger, and so is the scale of our language.
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:
One second is one second. A million seconds is 12 days. A billion seconds is 31 years. A trillion seconds is 31,688 years.
An inch is an inch. A million inches is 16 miles. A billion inches is 15,782 miles. A trillion inches is 15,782,828 miles.
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.