Millions, Billions, Trillions: How to Make Sense of Numbers in the News

National discussions of crucial importance to ordinary citizens – such as funding for scientific and medical research, bailouts of financial institutions and the current Republican tax proposals – inevitably involve dollar figures in the millions, billions and trillions.

Unfortunately, math anxiety is widespread even among intelligent, highly educated people.

Complicating the issue further, citizens emotionally undeterred by billions and trillions are nonetheless likely to be ill-equipped for meaningful analysis because most people don’t correctly intuit large numbers.

Happily, anyone who can understand tens, hundreds and thousands can develop habits and skills to accurately navigate millions, billions and trillions. Stay with me, especially if you’re math-averse: I’ll show you how to use school arithmetic, common knowledge and a little imagination to train your emotional sense for the large numbers shaping our daily lives.

Estimates and analogies

Unlike Star Trek’s Mr. Spock, scientists and mathematicians are not exacting mental calculators, but habitual estimators and analogy-makers. We use “back of the envelope” calculations to orient our intuition.

The bailout of AIG after the mortgage-backed securities crisis cost more than US$125 billion. The Panama Papers document upward of $20 trillionhidden in a dark labyrinth of shell companies and other tax shelters over the past 40 years. (The recently published Paradise Papers paint an even more extensive picture.) On the bright side, we recovered $165 million in bonuses from AIG executives. That’s something, right?

Let’s find out: On a scale where a million dollars is one penny, the AIG bailout cost taxpayers $1,250. The Panama Papers document at least $200,000 missing from the world economy. On the bright side, we recovered $1.65 in executive bonuses.

In an innumerate world, this is what passes for fiscal justice.

Let’s run through that again: If one penny represents a million, then one thousand pennies, or $10, represents a billion. On the same scale, one million pennies, or $10,000, represents a trillion. When assessing a trillion-dollar expenditure, debating a billion dollars is quibbling over $10 on a $10,000 purchase.

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