Count To One Million – GO!

How long do you think it would take you to count to a million? If you started now at the number 1 and counted one number higher each second until you got to a million, how long do you think it would take you to count to a million? To make calculations easier, you can use the CasioFX-991ES scientific calculator to work through this article to help you solve this fascinating real-life math problem.

Without giving it much thought, you may think that it would take a fair amount of time. However, time is such an abstract concept. Sometimes adults and even students do not have a clear and firm grasp on time. Any guesses before we start? 2 hours? 10 hours? You can find the worksheet to accompany this activity here.

ELEMENTS OF TIME

Most people know that there are sixty seconds in a minute and there are 60 minutes in an hour. Twenty-four hours make one day and there are 365 days in a year. However, when you start to quantify events into how long it takes, we often come up short.

For example, when you stand in line at the bank to make a payment, you feel like it takes hours, when realistically, only two minutes or 120 seconds have passed before you moved up one space. When we are eager for something to happen, often it feels like forever.

Most of the things we do that take a reasonable amount of time are often quoted in minutes or hours. How long did it take to drive from home to work? Oh about half an hour. How much time did you spend in your garden today? Maybe about 2 hours.

Rarely do we say “I spent 9000 seconds working on my homework. So we need a way to speak to that amount of time in a way that makes more sense to us. If we divide 9000 seconds by 60, we get 150 minutes. When we divide 150 minutes by 60 we get two and a half hours. Notice how the numbers started to quickly decrease from 9000 to 150 and then to 2.5

COUNT TO ONE HUNDRED

In order to try to determine how long it would take to count to one million, let us start out small. Let us try to count to one 100. If we determine that it will take us one second to count one number, then all we need to do is to divide by 60 to give us minutes

100 divided by 60 = 1.666

So it would take 1.666 minutes to reach 100. Notice how 100 seconds turned into a number of minutes that was not even 2? The decrease in quantity from seconds to minutes is amazingly fast. Notice that 100 seconds takes less than two minutes.

Since this does not seem like a lot, you may assume that counting to a million, which has a few more zeroes, would not be to much longer.

COUNT TO ONE THOUSAND

Let us try now with a larger number and one that is ten times as big as 100 – the number 1000. To convert one thousand seconds into minutes, all we need to do is to simply divide by 60.

1000 divided by 60 = 16.666

Notice that it would take 16.666 minutes to reach 1000. Did you also notice that when the original number was multiplied by ten (100 x 10 = 1000), that the answer also was multiplied by a factor of 10

100 seconds = 1.66 minutes

1000 seconds = 16.66 minutes

Now you are probably thinking, yes well adding a few more zeroes would not make that much of a difference. This is because as we consider the word ‘minutes’ we often relate it to things that don’t take much time to complete. Surely when we count to one million seconds, it will just take us a large number of minutes.

Let’s dig deeper.

COUNT TO TEN THOUSAND

Let us try now with an even larger number and one that is ten times as big as 1000 – the number 10,000. To convert ten thousand seconds into minutes, all we need to do is to simply divide by 60.

10,000 divided by 60 = 166.666

Now you are getting to the point where you are saying “well 166 minutes is more than 60 so now we are getting into hours”.

And you are right.

60 minutes = 1 hour

60 minutes also = 60 x 60 = 3600 seconds.

Let us try to convert 166.666 minutes into hours. HOW? By dividing by 60 since there are 60 minutes in an hour.

166.66 divided by 60 = 2.777hours

THERFORE at this moment, 10,000 seconds = 2.777 hours.

COUNT TO ONE HUNDRED THOUSAND

We are almost there. Let us try now with a number that is ten times as big as 10,000 – the number 100,000. To convert one hundred thousand seconds into minutes, all we need to do is to simply divide again as we have been doing all along by 60.

100,000 divided by 60 = 1666.666

Now we have reached over 1,666 minutes. We will need to divide this by 60 to get the number of HOURS this is equal to since one thousand six hundred sixty six minutes is a little hard for us to understand. Again, this is because not many things in our daily lives takes this amount of ‘minutes’ to complete.

1666.66 divided by 60 = 27.777 hours

Did you notice we have now reached over 24 hours. What is significant about 24 hours? Yes it is a whole day. Counting to 100,000 has taken three hours beyond an entire day. And this is if we never stopped doing anything else except counting!

COUNT TO ONE MILLION

We are almost there. Let us try now with our magic number – the number 1,000,000 (one million). To convert one million seconds into minutes, again we simply divide as we have been doing all along by 60.

1,000,000 divided by 60 = 16,666.666

Imagine – 16,666 minutes. Have you ever heard anyone talk about sixteen thousand minutes? So let us divide this by 60 to get the number of HOURS this is equal to.

16,666.66 divided by 60 = 277.777 hours

Is that right? 277 hours? Yes it is. So let us change that into days since we know every 24 hours is a day. We just divided by 24.

277.777 hours divided by 24 = 11.57 days.

YOU HAVE DONE IT!

Now you have solved the problem of how long it would take you to count to one million. Imagine starting on January 1. By the time you stopped, you would have gotten to January 12 and probably very tired and hungry.

This type of exercise helps you gain a deeper appreciation of time and how long it takes to complete a given activity. You can find the worksheet to accompany this activity here.

Just imagine how long it would take to reach a billion!

Trying learning how to multiply by 11 in your head by learning the secret math magic trick. You will fascinate others by your mental math ability.