The Power of 10

Any citizen who wants to vote responsibly needs to have a sense of proportion and be able to weigh the choices our democratic government is making quickly and easily.

You can practice thinking on your feet with large numbers, a different skill from what we were taught in primary school, so that you can calculate informed, fact-based opinions on which policies are winning and which may be bankrupt.

You need the ability to make approximate estimates involving large numbers, quickly in your head. The best news I ever heard was: you can multiply numbers by adding their exponents. Or divide them by subtracting their exponents. And the exponent is nothing more than the length of the number in digits. If the first digit is over 3, you can add a half. A painless way to get approximate answers to large-number problems in your head allows you to be more inventive and creative in considering all kinds of business and policy questions.

How can we reason with powers of 10 in real life? Let's use the California High Speed Rail proposal as an example. Most folks either support it because "I Like Trains", or oppose it because "I hate socialism". But a smart person should make a decision using a sense of proportion.

I always start by calculating the cost per person.

The total cost of CA high speed rail is projected to be $45 billion. Using exponents to estimate, remember that a billion is 9 digits. 45 billion adds another digit. Since 4 is larger than 3, you can add another half a digit, and about 1.6 digits. So that is about 10 to the 10.6 .

The California Population is 37 million, so that is about 10 to the 7.5.

To get cost/Californian simply subtract the exponents. 10.6 – 7.5 = 3.1.

Now 10 to the 4.1 is a bit more than $1,000 so we say $1,200 to be in the ballpark of cost of the High Speed Rail project per Californian. Now you have grounds for an informed decision in terms of cost. Some people would save money and carbon emissions if they invested $1,200 in a train. Many Californians will never travel between SF and LA and would be forced to make the same investment, instead of something that would help them with their daily commute. If you could save 10 million Californians 30 minutes a work day, and their free time is worth $8/hour then you have saved each $1000 per year in commuting costs, not counting fuel. That's worth (10^3 * 10&7 = 10&10 ) 10 billion dollars per year. So modest improvements in traffic and gridlock alleviation through commute traffic improvements can provide benefits to pay for themselves quickly.

For your next exercise, you may want to calculate the cost of the Iraq war in dollars per Iraqi. (Maybe 3 trillion dollars, 30 million Iraqis. 10^12.5 / 10^7.5 = 10^5 = 100,000 $/Iraqi.)

Or the cost per American of the 3 million dollar investment the DOE made in the very promising area of Airborne Wind Turbines. (10^6.5 / 10^8.5 = 10^(-2)). So we each spent about a penny on one of the most promising forms of renewable energy. These numbers are thought-provoking, and now they are comparable: do we want to spend:

• $1,200 per Californian on High Speed Rail?
• $100,000 per Iraqi on the Iraq war?
• $.01 per American on renewable energy?

Practice one of these back-of-the-envelope calculations every day and you will have the sense of proportion you need to know which policies to support and keep politicians accountable. It will serve you very well in business and personal finance. It is so easy once you get started!