10.1. Metric System
www.ck12.org
10.1 Metric System
Here you’ll learn how to measure length in metric units.
Have you ever wondered how to use metrics to measure the height of a plant? Remember Tania from the last
concept? Well, now Tania is working on growing tomato plants, and she will be using metric units of measurement.
Tania has decided to begin with tomatoes. It is early spring, so she knows that it is probably the best time to begin.
She has gathered her supplies and a pack of seeds. Tania begins reading the package and learns that there are all
kinds of measurement issues when planting seeds. The package says that she should plant each seed 3 mm deep.
Tania is wondering how deep she should plant each seed.
Guidance
In science classes, and anywhere outside of the United States, we measure length with the metric system. The most
common units that we use to measure length in this system are the millimeter, centimeter, meter, and kilometer. This
Concept will give you an overview of each measurement unit. Let’s take a look at each.
Millimeter
The millimeter is the smallest commonly used unit in the metric system. When we measure something in millimeters,
we use mm as an abbreviation for millimeter. A millimeter would be used to measure something that is very small,
like a seed.
Centimeter
98
www.ck12.org
Chapter 10. Measurements
The centimeter is the next smallest unit of measurement. To abbreviate centimeters we write cm (for example, 3 cm).
Centimeters are even smaller than inches. One centimeter is only the width of a staple. This ruler shows centimeters.
We can use a ruler to measure centimeters and millimeters. On many rulers, we can see both the customary
units of measurement and the metric units of measurement. You can see inches, centimeters and millimeters on
this ruler. What about when we have to measure something that is longer than a ruler? When we are measuring
something that is longer it doesn’t make sense to use centimeters or millimeters. We could use them, but it would
take a very long time to count all of those centimeters or millimeters. Instead, we can use two larger units of
measurement. We can use the meter and the kilometer.
Meters
The next metric unit we use is the meter. To abbreviate the meter we write m (for example, 8 m). A meter is longer
than a foot. Actually, a meter is just about the same length as a yard. One meter is roughly the length from your
finger tips on one hand to the fingertips on your other hand if you stretch your arms out to your sides. Go ahead and
try this right now with a peer. As you can see, one meter is much, much longer than one centimeter. It actually
takes 100 centimeters to equal one meter. We use meters to measure bigger objects or longer distances, such as the
depth of a pool or length of a hallway. We could use a meter stick to measure meters. A meter stick is exactly one
meter long.
This is a bit complicated, however, when an object or distance is several meters long. We have to make a mark on
the object being measured at the end of the meter stick, then move the meter stick down and make another mark
to show the next meter. It is easier to use a tape measure. Tape measures often show customary units (feet and
inches) down one side and metric units (centimeters and meters) down the other.
What about when we want to measure much longer distances and it doesn’t make sense to use meters? That
is when we use kilometers.
Kilometers
Kilometers are very long. To abbreviate the word kilometer we write km (for example, 12 km). Like miles, we use
kilometers to measure long distances, such as the distance from your house to the store or from one town to another.
Kilometers are only a little more than 1/2 as long as miles, but they are much longer than meters. In fact, there are
1,000 meters in a kilometer!
Here are a items for you to practice measuring using millimeters and centimeters. We will be working with meters
and kilometers a little later.
Example A
99
10.1. Metric System
www.ck12.org
Solution: 6 1/2 cm
Example B
Solution: 4 3/4 cm
Example C
A paper clip
Solution: Answers will vary. Check your measurements with a peer.
Now let’s go back to Tania. Tania takes a ruler and measures 3 mm on the plant pot. Then she plants the seed.
You can look at a ruler and find 3 mm on it. This will help you to see the length of Tania’s measurement.
Tania’s next concern is the length of the stem after germination. Tania does not want the stems to be long and
leggy. Tania decides to use inches to measure the stems as her plants grow. This way she can be sure that they
are the correct size when replanted.
Tania has started her tomato plants.
Vocabulary
Metric units of length
units of measurement such as millimeter, centimeter, meter and kilometer.
Millimeter
the smallest common metric unit of length
Centimeter
a small metric unit of length, best measured by a ruler
Meters
a unit compared with a foot or yard. 1 meter = a little more than 3 feet
Kilometer
a metric unit for measuring distances
100
www.ck12.org
Chapter 10. Measurements
Guided Practice
Here is one for you to try on your own.
Sasha is making a dress, however the pattern for the dress is measured in metric units. Sasha isn’t very familiar with
metrics, in fact, she isn’t sure which unit she should be using for the measurements. Given what you have learned in
this Concept, which metric unit should Sasha use? Which unit will make the most sense when she needs to purchase
material?
Answer
A meter can be compared to a little more than 3 feet or to a yard. Since material is often measured in yards, it makes
the most sense for Sasha to use meters.
Video Review
MEDIA
Click image to the left for more content.
KhanAcademyAdding Different Units of Length
Practice
Directions: Choose the appropriate unit of length using metric units for each item listed below.
1. The depth to plant a seed in the soil
2. The height of a tree
3. The area of a garden plot
4. The distance from a garden to the local farm store
5. The length of a carrot
6. A stretch of fencing
7. The length of a hoe
8. The distance between two seedlings planted in the ground
9. The height of a corn stalk
10. A road race
11. A grub collected from the garden
12. The width of a garden row
13. The length of a garden row
14. The size of a small seed
15. The distance that a tractor can travel on a large farm per day
101
10.2. Metric Prefixes
www.ck12.org
10.2 Metric Prefixes
• List common metric prefixes and their exponential values.
• Convert from one exponential factor to another for a given unit.
What do Latin and Greek have to do with modern science?
Isn’t it hard enough to learn English terms? For hundreds of years, the languages of the educated class were Latin
and Greek. In part, because the literature of philosophy was Latin and Greek. Even the medieval Bibles were written
in those two languages – the first English translation was in the late 1380s. Using Latin and Greek allowed scholars
from different countries to communicate more easily with one another. Today we still see many Latin phrases in
legal communications (“pro bono” meaning to do something “for the good” and not charge legal fees), scientific
naming of biological species, and Latin is used for the annual student speech at Harvard University graduations. Not
bad for a “dead” language.
Metric Prefixes
Conversions between metric system units are straightforward because the system is based on powers of ten. For
example, meters, centimeters, and millimeters are all metric units of length. There are 10 millimeters in 1 centimeter
102
www.ck12.org
Chapter 10. Measurements
and 100 centimeters in 1 meter. Metric prefixes are used to distinguish between units of different size. These
prefixes all derive from either Latin or Greek terms. For example, mega comes from the Greek word µégaV, meaning
“great”
The table below lists the most common metric prefixes and their relationship to the central unit that has no prefix.
Length is used as an example to demonstrate the relative size of each prefixed unit.
TABLE 10.1: SI Prefixes
Prefix
giga
mega
Unit Abbrev.
G
M
Meaning
1,000,000,000
1,000,000
kilo
k
1000
hecto
h
100
deka
da
deci
centi
d
c
10
1
1/10
1/100
milli
m
1/1000
micro
µ
1/1,000,000
nano
n
1/1,000,000,000
pico
p
1/1,000,000,000,000
Example
1 gigameter (Gm) = 109 m
1 megameter (Mm) = 106
m
1 kilometer (km) = 1000
m
1 hectometer (hm) = 100
m
1 dekameter (dam) = 10 m
1 meter (m)
1 decimeter (dm) = 0.1 m
1 centimeter (cm) = 0.01
m
1 millimeter (mm) =
0.001 m
1 micrometer (µm) = 10 6
m
1 nanometer (nm) = 10 9
m
1 picometer (pm) = 10 12
m
There are more prefixes - some of them rarely used. Have you ever heard of a zeptometer? You can learn more about
prefixes at http://www.essex1.com/people/speer/large.html.
There are a couple of odd little practices with the use of metric abbreviations. Most abbreviations are lower-case.
We use “m” for meter and not “M”. However, when it comes to volume, the base unit “liter” is abbreviated as “L”
and not “l”. So we would write 3.5 milliliters as 3.5 mL.
As a practical matter, whenever possible you should express the units in a small and manageable number. If you are
measuring the weight of a material that weighs 6.5 kg, this is easier that saying it weighs 6500 g or 0.65 dag. All
three are correct, but the kg units in this case make for a small and easily managed number. However, if a specific
problem needs grams instead of kilograms, go with the grams for consistency.
Summary
• Metric prefixes derive from Latin or Greek terms.
• The prefixes are used to make the units manageable.
Practice
Do the online metric system crossword puzzle at
103
10.2. Metric Prefixes
http://education.jlab.org/sciencecrossword/index.html
Click on “metric system” to get to the puzzle
Review
1.
2.
3.
4.
5.
What is the prefix for “thousand”?
What is the prefix for 0.01?
How would you write 500 milliliters?
How many decimeters in one meter?
You have a mass that weighs 1.2 hectograms. How many grams does it weigh?
• metric prefixes: Prefixes used to distinguish between metric units of different sizes.
104
www.ck12.org
www.ck12.org
Chapter 10. Measurements
10.3 SI Base Units
• Define the SI system of units.
• List the seven base units of measurement.
How long is a yard?
It depends on whom you ask and when you asked the question. Today we have a standard definition of the yard,
which you can see marked on every football field. If you move the ball ten yards, you get a first down and it doesn’t
matter whether you are playing in Los Angeles, Dallas, or Green Bay. But at one time that yard was arbitrarily
defined as the distance from the tip of the king’s nose to the end of his outstretched hand. Of course, the problem
there is simple: new king, new distance (and then you have to remark all those football fields).
SI Base Units
All measurements depend on the use of units that are well known and understood. The English system of measurement units (inches, feet, ounces, etc.) are not used in science because of the difficulty in converting from one unit to
another. The metric system is used because all metric units are based on multiples of 10, making conversions very
simple. The metric system was originally established in France in 1795. The International System of Units is a
system of measurement based on the metric system. The acronym SI is commonly used to refer to this system and
stands for the French term, Le Système International d’Unités. The SI was adopted by international agreement in
1960 and is composed of seven base units.
TABLE 10.2: SI Base Units of Measurement
Quantity
Length
Mass
Temperature
Time
Amount of a Substance
Electric Current
Luminous Intensity
SI Base Unit
meter
kilogram
kelvin
second
mole
ampere
candela
Symbol
m
kg
K
s
mol
A
cd
The first five units are frequently encountered in chemistry. All other measurement quantities, such as volume, force,
and energy, can be derived from these seven base units.
The map in Figure 10.3 shows the adoption of the SI units in countries around the world. The United States has
legally adopted the metric system for measurements, but does not use it in everyday practice. Great Britain and
much of Canada use a combination of metric and imperial units.
Summary
• The SI system is based on multiples of ten.
• There are seven basic units in the SI system.
• Five of these units are commonly used in chemistry.
105
10.3. SI Base Units
www.ck12.org
FIGURE 10.1
Meter standard.
FIGURE 10.2
Kilogram standard
FIGURE 10.3
Areas of world using metric system.
Practice
Use the link below to answer the following questions:
http://physics.nist.gov/cuu/Units/history.html
1.
2.
3.
4.
106
When was the metric system created?
What was deposited in the Archives de la République in Paris?
What was the CGS system based on?
When was the name International System of Units (SI) assigned?
www.ck12.org
Chapter 10. Measurements
Review
1. What does SI stand for?
2. When was this system adopted by the international community?
3. Which of the units are commonly used in chemistry?
•
•
•
•
English system: A system of measurements based on feet inches, and other somewhat arbitrary units.
The International System of Units: Based on the metric system of measurements.
Metric system: Based on units of 10.
SI: The metric system and stands for the French term, Le Système International d’Unités.
107
10.4. SI Length and Volume Units
www.ck12.org
10.4 SI Length and Volume Units
• Define length.
• Define volume.
• Describe standard measure of length and volume.
Back in the days before all the electronic gadgets sailors now have for measuring depth and locating undersea objects,
the fathom was the unit of measurement for depth. A rope was knotted every six feet and the end was dropped over
the side of the ship. You could tell how deep the water was by how many knots went under the water before the rope
hit bottom. Today we just turn on an instrument and read the depth to a high level of accuracy.
Length and Volume
Length is the measurement of the extent of something along its greatest dimension. The SI basic unit of length, or
linear measure, is the meter (m). All measurements of length may be made in meters, though the prefixes listed in
various tables will often be more convenient. The width of a room may be expressed as about 5 meters (m), whereas
a large distance such as the distance between New York City and Chicago is better expressed as 1150 kilometers
(km). Very small distances can be expressed in units such as the millimeter or the micrometer. The width of a typical
human hair is about 20 micrometers (µm).
Volume is the amount of space occupied by a sample of matter. The volume of a regular object can be calculated
by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units
of volume are derived from units of length. The SI unit of volume is the cubic meter (m3 ), which is the volume
occupied by a cube that measures 1 m on each side. This very large volume is not very convenient for typical use
in a chemistry laboratory. A liter (L) is the volume of a cube that measures 10 cm (1 dm) on each side. A liter is
thus equal to both 1000 cm3 (10 cm ⇥ 10 cm ⇥ 10 cm) and to 1 dm3 . A smaller unit of volume that is commonly
used is the milliliter (mL – note the capital L which is a standard practice). A milliliter is the volume of a cube that
measures 1 cm on each side. Therefore, a milliliter is equal to a cubic centimeter (cm3 ). There are 1000 mL in 1 L,
which is the same as saying that there are 1000 cm3 in 1 dm3 .
108
www.ck12.org
Chapter 10. Measurements
FIGURE 10.4
A typical water bottle is 1 liter in volume
FIGURE 10.5
Rubik’s cube. This Rubik’s cube is 5.7 cm on each side and has a volume
of 185.2 cm3 or 185.2 mL.
Summary
• Length is the measurement of the extent of something along its greatest dimension.
• Volume is the amount of space occupied by a sample of matter.
• Volume can be determined by knowing the length of each side of the item.
Practice
Read the section of length and volume in the link below and answer the following questions:
109
10.4. SI Length and Volume Units
www.ck12.org
FIGURE 10.6
Graduated cylinder. Volume in the laboratory is often measured with a
graduated cylinder, which come in a variety of sizes.
http://www.montgomerycollege.edu/Departments/biotp/Metric.html
1.
2.
3.
4.
What are some units of length in the metric system?
Do the first three length conversions.
Where on the meniscus do you measure volume in a graduated cylinder?
Do the first two conversion examples for volume.
Review
1.
2.
3.
4.
Define length.
Define volume.
An object measures 6.2 cm ⇥ 13.7 cm ⇥ 26.9 cm. Which value is the length of the object?
How big is a mL?
• length: The measurement of the extent of something along its greatest dimension
110
www.ck12.org
Chapter 10. Measurements
• meter: The SI basic unit of length, or linear measure
• volume: The amount of space occupied by a sample of matter. The volume of a regular object can be
calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we
say that units of volume are derived from units of length
111