There are many numbers that have an unlimited number of decimal places following the decimal point. The value of pi is one of them. The value of Pi begins this way:
3.1415926535
Following the digits shown above, there is an unlimited number of additional digits. I’m fascinated to contemplate this fact. No one will ever know all the decimal places of Pi because there is no end to them. It’s easy to find what are the first 10, the first one thousand, the first one million, etc. The Internet can give these to you. Even though a million digits are a great many, they are as nothing when you think that there is an unlimited number of them.
If you were to try to find out what is the very last one, you would not succeed. There is no last one. There is an infinite number of decimal places in the value of Pi.
At the time of this writing (October, 2011), the Internet states that the value of pi has been computed to over one trillion digits. It is almost as difficult to imagine a trillion digits as it is to imagine an unlimited number. On the Internet you can easily find one million digits for Pi. Browse through the list to get an impression of what a million digits looks like. Now try to image a number of digits that is a million times larger.
What proportion of one trillion is one million? This can be computed easily. It’s one millionth the size. (A million is a 1 followed by six zeroes; a trillion is a 1 followed by twelve zeroes.) What proportion of an infinite number is one million? There is no way to easily imagine a number of this size no matter how you try. What proportion of an infinite number is one trillion? This is truly impossible to imagine. There is no way to image what proportion of an infinite number any number is. It’s futile to try.
Why do I bring this up? I find the world of numbers a fascinating place. I’d like to inspire others to join me in discovering the many mysteries and wonders of numbers.