# A Brief Intermission for Large and Small

We are about to enter the world of the very large and the very small.  The universe is enormous; in fact, we don’t know whether it is infinite or has a boundary and probably never will because of the limits of how far we can see.  As best we can determine the universe is about 13.7 billion years old.  This puts an absolute limit on how far we can see: 13.7 billion light years.  A light year is the distance light travels in one year.  Light coming from any objects farther than 13.7 billion light years is undetectable simply because it hasn’t had time to get here yet.

A simulated view of the entire observable universe, approximately 14 billion light-years across. (Photo credit: Wikipedia)

In the terms we are going to speak, 13 billion is a small number.  Rather than write “a thousand billion” or “a billion billion” it helps to have some sense of the magnitude of those numbers by writing them in terms we can appreciate.  Just how big is a thousand billion?  Written out it would be 1,000,000,000,000.  A billion billion is 1,000,000,000,000,000,000.  Numbers like this convey more of a sense of the size of the number than the words “billion billion” but they are cumbersome to write.  Instead of writing numbers in this way, science uses scientific notation to express both very large and very small numbers.  Scientific notation writes numbers as powers of 10.  Ten to the first power is written as 101 and means 10 x 1.  Ten to the second power is 102 meaning 10 x 10 or 100.  Ten to the third power is 103 for 10 x 10 x 10 or 1,000.  One million (1,000,000) is written as 106.  As you can see, the number of zeroes that follows the one is the same as the power to which 10 is raised, three in the case of 103 (1,000) and six in the case of 106 (1,000,000).  In this way we can know that 1024 is a really big number and that it is bigger by 100 times than 1022 without having to count zeroes to see which number has more, or figuring out how many billion trillion that number is.

When it comes to very small numbers, scientific notation still raises 10 to a given power, but this time makes a fraction, such as 1/102 to represent 1/100 or .01.  However, to avoid 1/10, the number is written 10-2, the minus sign indicating that this is a fraction with 102 in the denominator.  Thus, one one-thousandth (1/1000) is written 10-3.  As with large numbers we can readily see that 10-6 is a very small number, one one-millionth (1/1,000,000).

So to give some perspective about how far 13.7 billion light years is, we can convert that to miles.  Light travels about 186,000 miles per second.  In a year there are 60 seconds/minute x 60 minutes/hour x 24 hours/day x 365 days per year, or 31,536,000 seconds.  For every second light travels 186,000 miles so a light year is 31,536,000 x 186,000 = 5.87 x 1012 miles.  Now multiply that by 13.7 billion (13.7 x 109) and you get an idea of how far away the “end of the universe” is: 80 x 1021 miles, or 80 followed by 21 zeroes.

While this post might remind you too much of high school, all you need to remember is that if ten is raised to a positive power (2, 5, 24, etc.) it’s a big number, while if ten is raised to a negative number (-2, -5, -24, etc.) it’s a small number and gets smaller as the power gets bigger in absolute terms.

With this technical background we can now start to talk about how the steady state proponents were finally vanquished by the big bang backers.

## 2 thoughts on “A Brief Intermission for Large and Small”

1. The only way to describe these numbers is astronomical. I can’t get my head round anything bigger than a thousand. And it’s getting bigger????

2. LOL – “I’m English major, you do the math” is my motto, but I actually learned some math here. Thanks 🙂