Large Numbers and One Million

Large numbers are seldom used by ordinary people like us. Most of our lives, we only use numbers less than 100. We usually have 3-5 siblings, 5-10 friends, 30-40 classmates per academic year, 80 books.

Money is probably the first quantity that we count in thousands. A baseball or basketball game will usually attract several thousands of people. Pound for pound Kings Manny Pacquiao and Floyd Mayweather will most likely attract hundreds of thousands of spectators in an open field, but you would probably better stay home if you’ll be standing a kilometer away from the ring.

The latter two situations involve larger numbers than usual.  Quantities larger than these are actually very hard to estimate unless we find a systematic way of counting.  For instance, it is hard to estimate the number of persons attending a basketball game if we do not know the area of the stadium.

Our inability to handle large numbers comfortably gives us reasons to convert it to other units. If it’s hard to measure in meters, then we convert it to kilometers or miles. It is probably impractical to measure the area of Australia in square meters.

How big is 1 million?

A large number which is very popular is probably 1 million.  Television games, singing contests, talent shows, usually give 1 million as grand prize. Several open math problems have 1 million dollars or pounds for those who can solve it. Grigori Perelman qualified for the Clay Mathematics for 1 million dollars, but unfortunately, he declined it.

Now, how big is 1 million?

Time

Let us talk about time.  How long is 1 million seconds? Well, 1 minute is 60 seconds, which implies that 1 hour is 3,600 seconds, and one day is 86,400 seconds.  We divide 1 million by 86,400. This makes 1 million seconds approximately equal to 11.5 days.

How about 1 million hours? There are 24 hours in one day. We divide 1 million by 24, gives us approximately 41,667 days, or approximately 114 years. This means that in our lifetime, it is likely that we will never reach 1 million hours. One  million days is 2,379.7 years. That means that from the time Christ was born (about 5 BC), we have not reached one million days yet.

Distance

How far is 1 million kilometers?

That’s pretty far. Driving a car at a speed of 100 kilometers per hour, you will travel 1,000,000 kilometers in 10,000 hours or 416.16 days – that’s around one year and two months. In fact, the diameter of the earth is 13,000 kilometers.  Assuming that the earth is a perfect sphere, the length of a great circle is about 40,820 kilometers. This means that to travel 1 million kilometers in a car running at a hundred kilometers per hour, you have to circle the earth about 17 times to travel 1 million kilometers.

Texts and Pages

How many pages is 1,000,000 characters, includes spaces, no pictures, 11 point Calibri font?

Using the MS Word word count feature, I discovered that a full text page (A4 size) is about 500 words. This means that 1,000,000 characters is about 2,000 pages (or 1000 pages if printed back to back).

Now, how thick is a book with 1,000,000 pages?

Since a book is always printed back-to-back, we only have 500,000 pieces of paper. I measured my book entitled The Grapes of Wrath, it’s approximately one inch and it has 500 pages or 250 pieces of paper. Hence, a 1 million-page book is 500000/250= 2000 inches or about 166 feet thick.

Now, that’s a very thick book!

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Photos:  Manny Pacquiao by Bryce Edwards, Making Money by Photos8.com, [Book Page] by mccun934