Hey, another kind of "over-under"!!

Just some food for thought to put the number one billion and history in perspective...

A billion seconds ago it was about 1976.

A billion minutes ago Jesus was alive.

A billion hours ago our ancestors were living in the Stone Age.

A billion days ago no creature walked the earth on two feet.

And a billion dollars lasts 8 hours and 20 minutes at the rate our

Government spends it.

There are many references for this on the web and I'm sure you've seen it before. You can check the accuracy (perhaps the last one is a little off!). I still like sharing this with students as it not only puts the concept of a billion in perspective but it does offer a wonderful application of 1-significant digit estimates, scientific notation and orders of magnitude. Can you imagine asking students to estimate that a billion seconds is roughly 32 years without a calculator!!

Where are these kinds of estimates currently in our math curriculum? More likely occurring in a science class? Do they belong somewhere in our classes or are they just amusing curiosities? You can guess where my thoughts lie!

## Saturday, January 31, 2009

### Was the First Super Bowl More or Less Than a BILLION Seconds Ago?

Posted by Dave Marain at 5:29 PM

Labels: 1-significant digit estimation, estimation, scientific notation

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## 5 comments:

Dave,

Strange, but true... If you had asked a UK citizen in January of 1967 whether 2009 would occur within a billion seconds, they would have said, "Yes."... If you ask them today if 1967 was within a billion seconds ago, they will say, "No."..

Why? Well, serindipitously for this post, just over a billion seconds ago (1975) the UK adopted the "American billion". Up until then, the "British Billion" was a million million or 10^12.

Next thing you know they will be using feet and inches and miles..... oh....wait... they do.

and I actually do know how to spell serendipitously, even if I don't always do so.

There is an exponential thing going on there, yes? At least with the 60's. Well it's basically what you said about powers of 10. Could be an interesting exponential or log graphing application activity.

Pat--

Thank you for that info! The web does break down those borders, doesn't it! Thinking back to my days of learning German and French, I seem to recall the word "milliarde" which translated to a billion, not a million, I believe. Languages can be confusing so when are we going to move to an international language? Wait a second, isn't math the universal language?

Kate--

I like your idea of graphing here. Do they still use log-log or semi-log graph paper which controls the scale of large numbers on the x- or y-axis?

Here's how I estimated 1 billion seconds ago mentally--

To convert sec into yrs using a method like "factor-label" we need to divide 10^9 by the following product:

60x60x24x365

I did the multiplication using 1-significant digit estimates--

60x60 = 36x10^2 approx = 4x10^3

Then 4x10^3 x 24 = 96 x 10^3 approx = 1 x 10^5;

10^5 x 365 approx = 10^5 x 400 =

4 x 10^7

10^9 can be rewritten as (10^2)(10^7) so we're dividing (100)(10^7) by 4x10^7 which produces an approx. of 25 years.

Since I rounded up twice in those products in the denominator, the actual answer is closer to 30 years of course, but this type of crude approximation still has some value IMO. Being off by 6 or 7 yrs is a far sight better than being off by a power of 10!! Further, students gain valuable experience in the practical application of the "rules" of exponents!

If we expected students to do some of these mental math exercises and had them practice a few from time to time I think they would enjoy the "power" of using their mind! OR am I the only one who would find this to be "fun"! Of course somebody reading this is probably thinking that most students could handle the powers of 10 but they couldn't do the basic multiplication in their heads like 24 x 4 = 96...

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