Metric Prefixes and Scientific Notation



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In this section:

  • The metric system
  • Metric prefixes
  • How to convert "regular numbers" into scientific notation

Overview:

Many of you have trouble with metric prefixes and scientific notation.  In this section, we'll start by learning why we have metric prefixes and what the metric prefixes are used for.  Toward the end, we'll talk about the wonders and joys of scientific notation.  Hold on to your hats!


The Metric System


If you already live in a country that uses the metric system (which is practically anywhere but the United States), you can probably skip right past this section to the part about scientific notation.  However, if you're an American, chances are you don't really have any idea about how to use the metric system.  Don't sweat it - we'll learn about it now.


Why use the metric system?


If you’ve been using nonmetric units your whole life, you may be wondering what’s so great about the metric system.  After all, you’re probably very happy being five feet, ten inches tall and weighing 175 pounds.  It’s nice knowing that the temperature in your house is 680.  What’s the big deal?

The problem is not that these units can’t be used, because clearly they can.  The problem is that it’s very hard to convert between these units.  For example, can you tell me how many inches tall you are?  Probably not.  However, using the metric system, this problem is very easy.


What are the common metric units?

The common metric units are:

Seconds:  The main unit of time, this is abbreviated as “s”.

Meters:  This is the main unit of distance, abbreviated as “m”.

Degrees Celsius:  The unit of temperature, abbreviated as “0C”.  Temperature can also be measured in Kelvins (K), which are found by adding 273 to the temperature in degrees Celsius.

Kilograms:  The unit of mass, abbreviated as “kg”.  This is kind of a weird one, because the prefix “kilo” means thousand, so “kilograms” means “thousand grams”.  You’d think that “grams” would be the unit of mass, but for some reason, it’s not.

Hertz:  The unit of frequency, abbreviated as (Hz).  If something happens once a second, it happens with a frequency of 1 hertz.  
Joule:  The unit of work/energy, abbreviated as (J).

Pascals:  The unit of pressure, abbreviated as (Pa).  There are 101,325 pascals (101.325 kPa) in 1 atmospere.


Some handy conversion factors:

  • seconds to minutes:  There are 60 seconds in 1 minute
  • meters to inches:  There are 0.0254 meters in 1 inch
  • centimeters to inches:  There are 2.54 centimeters in 1 inch
  • kilograms to pounds:  There are 2.21 pounds in 1 kilogram
  • pascals to atmospheres:  There are 101.325 pascals in 1 atmosphere
  • kilopascals to atmospheres:  There are 101.325 kPa in 1 atm.
  • joules to calories:  There are 4.184 joules in 1 calorie

 


Metric Prefixes:


The following prefixes are used to make metric prefixes easier to work with.  For example, it’s not too handy to say that you live 345,000 meters from your grandparents.  It’s much nicer to say that you live 345 kilometers away:

Below, for your enjoyment, is a table that will allow you to use the more common prefixes like a star:

Prefix (symbol)

What it means

Example

nano (n)

10-9

0.000000001 meters = 1 nm

micro ( )

10-6

0.000001 meters = 1 m

milli (m)

10-3

0.001 meter = 1 mm

centi (c)

10-2

0.01 meter = 1 cm

deci (d)

10-1

0.1 meter = 1 dm

kilo (k)

103

1,000 meters = 1 km

mega (M)

106

1,000,000 meters = 1 Mm

giga (G)

109

1,000,000,000 meters = 1 Gm

 


Scientific notation:


Scientific notation is another way to express very large or very small numbers so that they’re more understandable.  It’s easier to say that a speck of dust weighs 1.2 x 10-6 grams than to say it weighs 0.0000012 grams.

To convert any number to scientific notation, follow these steps:

1)  Convert the number you’re converting into a number between 1 and 10 by moving the decimal either to the left or to the right.

Examples:

  • 45,000 is converted to 4.5 by moving the decimal four spaces to the left
  • 0.00045 is converted to 4.5 by moving the decimal four spaces to the right


2)  Write the number that you came up with in step one, followed by “x 10”.

Examples:

  • 45,000 = 4.5 x 10
  • 0.00045 = 4.5 x 10


3)  Recall how many decimal places you moved the decimal point in step one.  If the number that you’re converting is greater than 10, write a positive number as a superscript above the “x 10” from step 2.  If the number you’re converting is less than one, write a negative number.


Examples:

  • 45,000 = 4.5 x 104
  • 0.00045 = 4.5 x 10-4

And that’s all there is to it!


 

Comments, questions, random praise?  Email it to me at misterguch@chemfiesta.com


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