Lesson I: The Metric System and SI Units

	A meter is 3.37 inches more than a yard.
	A liter is 1.82 fluid ounces more than a quart.
	A dime weighs about one gram.

Introduction

The metric system is the preferred system of scientific units for several reasons:

The majority of countries in the world employ the metric system of measurement.
The prefixes attached to metric units carry the same meaning for all base units.
The metric system is based upon powers of ten, which is convenient because:
- A measurement in the metric system that is represented by a rational number remains a rational number after metric unit conversion. (For example, 250 mm = 25 cm = .25 m). In contrast irrational unit systems , such as the English system, do not have the same property (For example, 250 inches = 20.8333... ft = 0.0039457... mile)
- Because metric units are decimal-based, they are easily converted by moving the decimal point.

The terms mass and weight are often used interchangebly in chemistry. Strictly speaking, weight is the force (F) associated with a given mass (m) as it is accelerated (a) by gravity: F = m × a The English System unit of mass is the slug, which when multiplied by the acceleration of gravity (32 ft/sec²) gives the weight in pounds.

Metric Base Units

The metric system uses the following base units:

Unit of Measurement	Name	Abbreviation
Length	Meter	m
Mass	Gram	g
Volume	Liter	L

Frequently the above units are too small or more often too large to appropriately scale the measured quantity. It is then necessary to subdivide or expand our measurement unit. This will be discussed in the section on prefixes.

The liter is not the SI unit of volume Volume is a unit derived from length. The volume (V) of a cube that has length (l) = 1.0 cm, width (w) = 1.0 cm, and height (h) is given by: V = l × w × h
= 1.0 cm × 1.0 cm × 1.0 cm
= 1.0 cm³

By definition, 1.0 cm³ = 1.0 mL

It follows from dimensional analysis that 1.0 dm³ = 1.0 L.

SI Units

The metric-based Système International or SI units are used to standardize the report or calculation of scientific quantities:

Physical Quantity	Name of Unit	Abbreviation
Length	Meter	m
Mass	Kilogram	kg
Temperature	Kelvin	K
Time	Second	s
Amount of Substance	Mole	mol
Electric Current	Ampere	I
Luminous Intensity	Lumen	I_v

The SI units are used to construct all other units (these are called derived units). Some examples:

Property	Symbol	Dimensions	Name
Velocity	v	m · s^-1
Area	A	m²
Frequency	v	s^-1	Hertz (Hz)
Force	F	kg · m · s^-2	Newton (N)
Energy	E	kg · m² · s^-2	Joule (J)

Outside the United States, the word "meter" is spelled "metre" and the word "liter" is spelled "litre."

Metric Prefixes

To change the scale of the base units, prefixes are attached. A prefix represents a factor by which the base unit must be multiplied. Metric prefixes are listed below (The prefixes most-commonly used in chemistry are listed in red):

Prefix Symbol Decimal Value Power of Ten

Exa- E 1,000,000,000,000,000,000
10¹⁸

Peta- P 1,000,000,000,000,000
10¹⁵

Tera- T 1,000,000,000,000
10¹²

Giga- G 1,000,000,000
10⁹
Mega- M 1,000,000
10⁶
Kilo- k 1,000
10³
Hecto- h 100
10²
Deka- da 10
10¹
(no prefix)
1
10⁰
Deci- d 0 .1 10^-1
Centi- c 0 .01 10^-2
Milli- m 0 .001 10^-3
Micro- µ 0 .000001 10^-6
Nano- n 0 .000000001 10^-9
Pico- p 0 .000000000001 10^-12
Femto- f 0 .000000000000001 10^-15
Atto- a 0 .000000000000000001 10^-18

In addition to the base metric units, many other scientific quantities also employ this system of prefixes:

	1 Mb = 1 Megabyte = 1 × 10⁶ byte
	1 Food Calorie = 1 kcal= 1 kilocalorie = 1 × 10³ calorie
	1 ns = 1 nanosecond = 1 × 10^-9 second
	1 pf = 1 picofarad = 1 × 10^-12 farad
	1 kWH = 1 kiloWatt·hour = 1 × 10³ Watt·hour

The metric prefixes can be employed to scale the base units so that they can represent anything from a very large numeric value (for example by using prefixes such as Exa, Tera, or Mega) to a very small numeric value (for example by using prefixes such as Atto, Femto, or Pico). Scaling the unit up or down when reporting measurements is good practice because:

It can be used to keep the numeric value of measurements to reasonably-sized numbers, say between values of 0.01 to 100.
It can be used to remove ambiguous place-holding zeroes in measurments, so that the number of significant figures are properly represented.

The prefixes instantly convey how many decimal place moves are required of the numeric value. For example, using the scientific notation value of the metric prefixes):

1 cm = 1 centimeter = 1 × 10^-2 meter = 0.01 meter
1 kg = 1 kilogram = 1 × 10³ gram = 1000 gram
1 µL= 1 microliter = 1 × 10^-6 liter = 0.000001 liter

For further explanation of unit interconversion using the metric prefixes as conversion factors, visit the dimensional analysis page.

In addition to the standard metric prefixes, the Ångstrom is also a commonly used unit that arises in measurements on the atomic scale:

1 Ångstrom = 1 Å = 1 × 10^-10 meter

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