Units

English System Metric System Metric System Prefixes Mass vs. Weight
SI Units Derived SI Units Non-SI Units Unit Conversions

The English System of Units

There are several systems of units, each containing units for properties such as length, volume, weight, and time. In the English system the units are defined in an arbitrary way.

Length: inch (in), foot (ft), yard (yd), mile (mi)
12 in = 1 ft 5280 ft = 1 mi
3 ft = 1 yd 1760 yd = 1 mi
Volume: fluid ounce (oz), cup (c), pint (pt), quart (qt), gallon (gal)
2 c = 1 pt 32 oz = 1 qt
2 pt = 1 qt 4 qt = 1 gal
Weight: ounce (oz), pound (lb), ton
16 oz = 1 lb 2000 lb = 1 ton
Time: second (s), minute (min), hour (h), day (d), year (y)
60 s = 1 min 24 h = 1 d
60 min = 1 h 3651/4 d = 1 y

 

Practice Problem 1

Convert 6.5 feet into inches.

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The Metric System

The Metric System is based on the fundamental units of measure for length, volume, and mass.

Length: meter (m)
Volume: liter (L)
Mass : gram (g)

Base units in the Metric System can be converted into units that are more appropriate for the quantity being measured by adding a prefix to the name of the base unit. The common metric prefixes are given below.

Metric System Prefixes

Prefix Symbol Meaning
femto- f x 1/1,000,000,000,000,000 (10-15)
pico- p x 1/1,000,000,000,000 (10-12)
nano- n x 1/1,000,000,000 (10-9)
micro- x 1/1,000,000 (10-6)
milli- m x 1/1,000 (10-3)
centi- c x 1/100 (10-2)
deci- d x l/10(10-1)
kilo- k x 1,000 (103)
mega- M x 1,000,000 (106)
giga- G x 1,000,000,000 (109)
tera- T x 1,000,000,000,000 (1012)

The base units of length and volume are linked in the metric system. By definition, a liter is equal to the volume of a cube exactly 10 cm tall, 10 cm long, and 10 cm wide. Because the volume of this cube is 1000 cubic centimeters and a liter contains 1000 milliliters, 1 milliliter is equivalent to 1 cubic centimeter.

1 mL = 1cm3

The base units of volume and weight are also linked. The gram was originally defined as the mass of 1 mL of water at 4 degrees Celsius.

1g = 1mL H2O at 4 C

Practice Problem 2:

Convert 0.135 kilometers into meters.

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Mass Versus Weight

Mass is a measure of the amount of matter in an object, so the mass of an object is constant.

Weight is a measure of the force of attraction of the earth acting on an object. The weight of an object is not constant.

Mass is a more fundamental quantity than weight. There is no English equivalent to the verb weigh that can be used to describe what happens when the mass of an object is measured. You are therefore likely to encounter the terms weigh and weight for operations and quantities that are more accurately associated with the term mass.

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SI Units of Measure

In 1960 the International System of Units was proposed as a replacement for the Metric System. The seven base units for the SI system are given below.

SI Base Units

Physical Quantity Name of Unit Symbol
length meter m
mass kilogram kg
time second s
temperature kelvin K
electric current ampere D
amount of substance mole mol
luminous intensity candela cd

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Derived Si Units

The units of every measurement in the SI system must be derived from one or more of the seven base units. Some of the common derived SI units used in chemistry are given below.

Common Derived SI Units in Chemistry

Physical Quantity Name of Unit Symbol
density kg/m3
electric charge coulomb C (A s)
electric potential volt V (J/C)
energy joule J (kg-m2/s2)
force newton N (kg-m/s2)
frequency hertz Hz (s-1)
pressure pascal Pa (N/m2)
velocity (speed) meters per second m/s
volume cubic meter m3

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Non-SI Units

Strict adherence to SI units would require changing directions such as "add 250 mL of water to a 1-L beaker" to "add 0.00025 cubic meters of water to an 0.001-m3 container." Because of this, a number of units that are not strictly acceptable under the SI convention are still in use. Some of these non-SI units are given below.

Non-SI Units in Common Use

Physical Quantity Name of Unit Symbol
volume liter L (10-3 m3)
length angstrom D (0.1 nm)
pressure atmosphere atm (101.325 kPa)
torr mmHg (133.32 Pa)
energy electron volt eV (1.601 x 10-19 J)
temperature degree Celsius EC (K - 273.15)
concentration molarity M (mol/L)

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Unit Conversions

Length
1 m = 1.094 yd 1 yd = 0.9144
Volume
1 L = 1.057 qt 1 qt = 0.9464
Mass
1 g = 0.002205 lb 1 lb = 453.6 g

 

Practice Problem 3

The record for the Kentucky Derby is held by Secretariat, who ran the 10 furlongs in 1 minute, 59.4 seconds. Calculate his average speed in miles per hour.

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Practice Problem 4

Calculate the volume in liters of a cubic container 0.500 meter tall.

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Practice Problem 5

What is the value of a gold ingot 20.0 cm long by 8.5 cm wide by 6.0 cm tall, if the mass of a cubic centimeter of gold is 19.3 grams and the price of gold is $356 per ounce?

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Units | Errors | Significant Figures | Scientific Notation

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