Seconds in 1000 Years

Date: 02/13/2002 at 23:01:57
From: Chris Murdock
Subject: Pre-algebra

I need to know how many seconds are in one thousand years, including 
leap years. I just don't know how to figure it out. I really hope you 
can help me.

Date: 02/14/2002 at 09:44:36
From: Doctor Ian
Subject: Re: Pre-algebra

Hi Chris,

Nominally, a year is a leap year if it is divisible by 4. There are 
25 years like that in every century, which makes 250 over the course 
of 1000 years. However, years that are divisible by 100 are NOT leap 
years. There are 10 of those, which takes us back down to 240. 
But wait - if a year is divisible by 400, it IS a leap year.  

The problem here is that the number of years divisible by 400
depends on _which_ 1000 years you're looking at.  For example, 
if you're looking at the years from 2000 to 3000, you have 
three such years: 2000, 2400, 2800.  But if you're looking at
the years from 2100 to 3100, you only have two such years. 

So you could handle this in a couple of different ways.  One would 
be to say:

  The number of days in 1000 years is 1000 times 365, plus 250, 
  minus 10, plus either 2 or 3, depending on which 1000 years
  we're talking about.  
  
That would give us either 365242 or 365243 days in 1000 years. 
There are 24 hours in each of those days, 60 minutes in each of 
those hours, and 60 seconds in each of those minutes. A little bit 
of multiplication should give you the answer you're looking for. 

A second way to approach it would be to say:

  The number of days in 400 years is 400 times 365, plus 100,
  minus 4, plus 1, regardless of which 400 years we're talking
  about.  
  
So this tells us that there are 146097 days in 400 years.  If we 
multiply that by 2.5, we get 365242.5 days, which we can use as 
an estimate of the number of days in 1000 years.  (Note that this
is halfway between our other two values, so really we're just 
splitting the difference.)

Note that this leaves out the occasional 'leap second' that is added 
or subtracted to account for the fact that the period of rotation of 
the earth isn't constant. But I'll bet your teacher doesn't know about 
them. I only know about them because I used to work at NASA, where 
part of my job was to keep track of things like this.

Another bit of trivia that I picked up at NASA is this:  To within 
1 percent, the number of seconds in a year is pi*10^7, which is about 
31 million seconds. So if you don't get an answer about that size, you 
should go back and check your work.

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/