How many seconds in a decade?

Someone asked me recently, how many second in a decade? I reached for the calculator, and he said, “No, do it in your head, estimate.”

“Ah,” I thought, “a brain teaser, I love these!”

If you whip out a calculator, I’m sure you could answer the question quickly. Pen and paper, and you can do some long multiplication and figure it out withing a few minutes. What about in your head? Estimation is a powerful tool, something we can all learn. The trick is to start with simple mathematics you can do in your head, and round up, down and make assumptions. It can be fun to learn and practice.

Tip: I find it helps to talk the calculation out loud.

So, to the task, how will we estimate the number of seconds in a decade in our head?

Step one: How many seconds in an hour?
I know is there are 60 seconds in a minute, and 60 minutes in an hour. 60*60 is not a hard calculation to do in your head. Just multiple 6*6 and add two zeroes to the end. 6*6=36, tag on two zeroes and we’re at 3600. K, so 3600 seconds in an hour.

Step two: How many seconds in a day?
From step one, we know there are 3600 seconds in an hour. 3600 * 24 = number of seconds in a day. A little harder to do in your head, but we can estimate. The trick is to multiple numbers you know. Round the numbers down to something easy to multiply, get the answer. Round the numbers up to something easy to multiply, get the answer. The real answer is in between the two numbers you came up with.

Let’s try it. Do this in your head:
3000 * 20 = 60,000 (3*2=6, add 4 zeroes)
4000 * 30 = 120,000 (4*3=12, add 4 zeroes)

So, the number of seconds in a day is between 60K and 120K. Let’s split the difference and estimate 90K seconds in a day.

Step three: How many seconds in a year?
From our last step, we estimated 90K seconds in a day. 90,000 * 365 = number of seconds in a year. Let’s use the same estimation trick:
90,000 * 300 = 27,000,000 (9*3, add 6 zeroes)
90,000 * 400 = 36,000,000 (9*4, add 6 zeroes)

Let’s split the difference and say there are 31,000,000 seconds in a year.

Step three: How many seconds in a decade?
Easy, 31 million * 10 = 310 million. We estimate there are 310 million seconds in a decade.

Now, whip out the calculator and see how close we are. You can practice math estimation all the time. It’s especially fun to keep busy while driving with this, but keep a safe distance from the car ahead of you!

Dave.