**Metric Prefixes and Scientific
Notation**

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practice worksheets**

**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

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 |
0.000000001 meters = 1 nm |

micro (µ ) |
10 |
0.000001 meters = 1 µm |

milli (m) |
10 |
0.001 meter = 1 mm |

centi (c) |
10 |
0.01 meter = 1 cm |

deci (d) |
10 |
0.1 meter = 1 dm |

kilo (k) |
10 |
1,000 meters = 1 km |

mega (M) |
10 |
1,000,000 meters = 1 Mm |

giga (G) |
10 |
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 10
^{4} - 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 **