Making Sense of Numbers: Practical Comparisons

Many people who want to study economics get confused about the scale of numbers. Understanding the scale of a number adds context and invites comparisons, which leads to the question “does it make a difference?”. Understanding scale may seem like a mathy thing, but it is really about communication.

This post is motivated by a recent headline “Russia fines Google $20,000,000,000,000,000,000,000,000,000,000,000”.

That would be “twenty decillion US dollars” or about “28 decillion Canadian dollars”. Regardless of how much profit Google earns, the number is just stupid. It is much, much, much, much, much, much bigger (i.e., much more than 1000 times or even 1,000,000,000 times bigger) than the world’s annual GDP (about 110 trillion US dollars).

Conveying scale meaningfully aids communication. If somebody tells you a number, it is easier to remember if it has context. If you are trying to explain to somebody else why they should care about a number, try linking it to something that they care about.

Poor attempts at communicating scale sound like “$1,000,000 represents a line of $10 bills which is … long“. Since I do not know how many miles, meters or kilometers of $10 bills is equivalent to $100, I certainly do not understand something which is 10,000 times bigger.

Better examples include

• 100 (or sometimes 1.00) is often used as a reference point. The current value of the Consumer Price Index is 161.1, which means that it is about 60 percent higher than in the “base year” (which is 2002).
• 1000 is about number of hours of sleep in 125 days (or 1/3 of a year) or, based on one website, about 20 years-worth of clothing purchases https://pirg.org/articles/how-many-clothes-are-too-many/
• 1,000,000 (million) is 66,666.7 hours of work (pre-tax) at $15 per hour or 10 years of work if your annual salary is $100,000. (Oops: How many hours of work in 10 years?)
• 1,000,000,000 (billion) is about equal to the revenue that Amazon receives in half a day, or Walmart’s profit over about 24 days.
• 1,000,000,000,000 (trillion) is less than one-half of Canada’s annual GDP.   or 1/30th of the annual GDP in the US.
• 1% (i.e., “percent”= “per hundred”) is about half of the current inflation rate or an 1% increase in the number of new cars sold in a year in Canada https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=2010000201 is about 17,500.

A website offers more comparisons. The online comic strip xkcd offers some thoughts on numbers, “large” numbers, -illion numbers and garbage math.

Understanding numbers matters because some numbers in the news are wrong or omit context. A BBC podcast regularly answers questions from people who hear something and ask “is that number plausible?”

You may also notice that the better examples use a lot of rounding. The meaning of a number is rarely associated with its fifth decimal place. If you decide that it is important then you can use a calculator.

Now, it is your turn to write.  

• Pick an interesting number in the news and compare it with something numerical that is personally relevant.
• Effective communication depends on what the audience understands. So, what comparison would you use if you were talking with i) a CEO of a large company? ii) 25-year-old male? iii) 40-year-old female? iv) 60-year-old married couple? v) a 10 year old child?
• In the context of carbon emissions, people talk about gigatons of CO2. I understand that giga= billion and ton= heavy. So, I understand that gigaton= a lot. Can you provide a meaning or a personal scale to a gigaton?