Millions and Billions

I need your help visualizing millions and billions.

Date of Meeting:

In a recent interview on Innovation Hub, the mathematician and educator Steven Strogatz reflected on math education (specifically the requirement for students to study algebra) and the level of number in the general public:

“We don’t do a very good job of teaching what you might think of as numeracy, that is, the use of arithmetic [in the real world]. So, here’s an example: In current political discussion, there is a lot of talk from Senator Sanders about millionaires and billionaires, right?

Leaving aside the politics of what you think of what he’s saying, let me just talk about those numbers, million vs. billion, because in English they sound like almost the same number, both incomprehensible. They only differ in one letter, m vs. b, but I have to say that it always grates on me when he says those two things because millionaires and billionaires are really different and I can make you understand that if you don’t have a visceral feel for it by asking, do you have any sense of what a million seconds would be? Like how long would you have to wait for a million seconds to tick by?

A million seconds turns out to be about 11 1/2 days, so it’s a little less than two weeks. Okay, not you have a feeling about what that is. If I tell you a billion seconds is about 32 years, that’s a big fraction of your lifetime, whereas two weeks is not much of your lifetime. So, when someone says millionaires and billionaires, you should be thinking that’s the difference between 2 weeks and 32 years. They’re not comparable.

So, shame on Senator Sanders for saying that, because he’s really talking about billionaires. Anyway, I happen to like Senator Sanders and what he’s saying, so I’m not making a political point. But my point was more a numerical point, that because we don’t teach people things like number sense often enough, we just teach how to calculate, I think a lot of people are missing things that would make them be better citizens.”  

A few of us at CUNY are working on a HSE science curriculum on evolution. One of the first lessons involves students making a timeline of the history of Earth. The planet formed 4.6 billion years ago. Life began 3.6 billion years ago. First vertebrates show up 500 million years ago. Man arrives .2 million years ago. The difference between millions and billions really matters if you want students to understand the span of time evolution has operated in.

So, here’s my request for help. Strogatz shared a great way of visualizing the difference between millions and billions. What are some other ways? What have you done with students to help them get a visceral sense of these numbers? What other ways can you imagine? (Enter your ideas in the comments below. You can also write your ideas directly in this Google Doc.)

I’ll be compiling a list of visualizations and will come back in a few weeks to share.

2 thoughts on “Millions and Billions”

  1. I’m not sure if I like either of these more than what you are starting with, but:

    1 million minutes is about two years.
    1 billion minutes is about 2000 years.

    1 million dollars in hundred dollar bills weighs about 20 pounds.
    1 billion dollars in hundred dollar bills weighs about 20,000 pounds.

    A stack of a million one dollar bills is about 358 feet tall.
    A stack of a billion one dollar bills is about 68 miles tall.

  2. Nice! Here a few others:

    A million calories would be eaten in 1.4 years (at 2,000/day).
    A billion calories would be eaten in 1,400 years.

    A million grains of rice weighs about 35 lbs.
    A billion grains of rice weighs about 17.5 tons.

    A million heartbeats would take about 9 days.
    A billion heartbeats would take about 24 years.

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