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### A Billion Seconds

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Date: 10/21/96 at 12:47:59
From: Anonymous
Subject: When a Billion Seconds

If I was born on 01/02/84, on what day and what year, month will I
have been alive for a billion seconds?
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```
Date: 10/22/96 at 10:52:8
From: Doctor Ken
Subject: Re: When a Billion Seconds

Hi Alvina -

To solve this kind of problem, you need to first figure out how many
seconds there are in an hour, in a day, in a week, in a year, and so
on.  To really do this problem right, you'd have to take into account
leap years (which can get pretty complicated - they don't just happen
every 4 years; there are some other rules that they follow) and leap
seconds (yup - they happen!).

But in this solution, I'm not going to take these factors into
account, so that you can see the general strategy behind how you'd
solve this problem.

Okay, here we go!  There are 60 seconds in a minute, and 60 minutes
in an hour.  So there are 60 x 60 seconds in an hour, in other words
3600 seconds in an hour.  Furthermore, there are 24 hours in a day,
so there are 24 x 3600 seconds = 86400 seconds in a day.  Also, there
are 365 days in a year, so there are 365 x 86400 seconds = 31,536,000
seconds in a year.  Let's summarize this in a table:

1 hour = 3600 seconds
1 day  = 86400 seconds
1 year = 31,536,000 seconds

So how many years does it take to reach 1,000,000,000 seconds?  Well,
31 x 31,536,000 =   977,616,000 and
32 x 31,536,000 = 1,009,152,000.

So 31 years is not enough, and 32 years is too much.  Looks like it's
going to be 31 years plus a little bit.

How much?  Well, 1,000,000,000 - 977,616,000 = 22,384,000.  So we need
to figure out how many months and days that is.  I'll leave this part
of the problem for you to figure out - it can be a little tricky to
figure out how many seconds are in each month, but you can use the
figure we found above, the number of seconds in a day, to figure this
out.  Good luck!

-Doctor Ken,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Calendars/Dates/Time
Middle School Puzzles

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