### Scientific Notation and Metric Prefixes

Have you ever seen the notation 10-2 or something similar?  This is called Scientific Notation.  Scientific Notation is a way to write a very small number easily.

It’s really quite a pain to write 0.00000000004522 three times in your calculations and sometimes they won’t even fit in your calculator.

## Scientific Notation

For this reason, scientists have decided to make a form called “Scientific Notation” to write really small or really large numbers.  To easily write this number you count the values to the right of the decimal.  How many decimal places (not numbers) are there to the right of the decimal?  (There are 14).

Now, how many are there to the right of the decimal until you count up to the number four?  (There are 10).  Now go past four and stop (There are 11). This is the number you want to use as scientific notation, you want to count past one non zero digits and stop.  Below are the rules for scientific notation:

If you are trying to put a really small number in scientific notation, it will be 10x

If you are trying to put a really large number in scientific notation, it will be 10x

Where X is the number of decimal places until you reach a non zero number and add one to this number.

Therefore, we can see that the answer to 0.00000000004522 would be 4.522 x 10-11.

### How about a really large number?

Let’s try 23,000,000.   We’ll count to the left this time until we reach a non zero digit, and go one past.   There are seven shifts.  Therefore, following the rule above, this would be 2.3 x 107.

## Doing Scientific Notation on your Calculator

Almost all calculators have a scientific notation button.  Usually, the key is denoted as a “EE”.  You can use this key to log in really small or really large numbers like the ones above.  If your calculator does not have a scientific notation key, get a different calculator.  I use a TI-30XA and I find it’s perfect for chemistry.

### Chemistry Unit Conversions and Metric Conversions

You were probably thinking to yourself that the problems above have nothing to do with chemistry.  We’re getting to that.  Chemists like to use metric prefixes instead of English units (the units used in the United States).

This is because the metric system works in the power of ten, and it’s a lot easier to work with than the English system.  What does this mean?  It means you need to memorize a few simple metric prefixes.  Below are the following:

 Prefix Scientific Notation Value tera- 1012 giga- 109 mega- 106 kilo- 103 hecto- 102 deka- 101 deci- 10-1 centi- 10-2 milli- 10-3 micro- 10-6 nano- 10-9 pico- 10-12 femto- 10-15

You’ll find when you are doing conversions you’ll be asking yourself, which gets the scientific value?  If I convert meters to millimeters, which gets the 10-3 prefix?

The simple answer is always to use the prefix with the base value, or in this case, meters.  This will keep everything straight.  I’ll show you what I mean in problem 1.3.

Problem 1
Problem: Convert 112 nanometers to meters

Plan: We’ll perform unit conversion to convert nanometers to meters using the above table.

Answer:  1.12 e-7 Meters Discussion: Did you see where you could get confused?  Does the 10-9 go on the meters or on the nanometers?  If you want to put it on the prefix side, you need to change the sign.  Therefore, whenever I’m doing these conversions, I always put the scientific value with the base unit side and keep it the way I memorized it.

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