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The Metric System and Measurement
Introduction
The metric system is the world standard for measurement. Not only is it used by scientists
throughout the world, but most nations have adopted it as their standard of measurement. All of the
measurements done in this course will use the metric system.
The table below shows the standard unit of length, weight, volume, and temperature in the metric
system. It also shows the English equivalent.
Metric
English
Length
meter
39.37 inches
Weight
gram
0.03527 ounces
Volume
liter
1.0567 quarts
Temperature degree (Centigrade) 1.8 degrees Fahrenheit
Meters, grams, and liters (see the table above) form the basis for larger or smaller units. The units
are named using these prefixes:
Kilo = 1000
Deci = 1/10
Centi = 1/100
Milli = 1/1,000
Micro = 1/1,000,000
Nano = 1/1,000,000,000
The table below shows how meters are related to five other measures of length. Unit
Length
kilometer (km)
1,000 m (1 X 103 m)
meter (m)
1m
centimeter (cm) 0.01 m (1 X 10-2 m)
millimeter (mm) 0.001 m (1 X 10-3 m)
micrometer (um) 0.000001 m (1 X 10-6 m)
nanometer (nm) 0.000000001 m (1 X 10-9 m)
Notice that each of the units in the table above are related to meters by a multiple of 10.
The photograph below shows the end of a meter stick. The 90 cm mark can be seen in the center of
the photograph. One meter = 100 cm. Notice that each centimeter is divided into 10 mm.
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The tables below show similar units based on grams (weight) and liters (volume).
Unit
Weight
metric ton (t)
1,000 kg or 1,000,000 g (1 X 106 g)
Kilogram (kg) 1,000 g (1 X 103 g)
gram (g)
1 gram
milligram (mg) 0.001 g (1 X 10-3 g)
microgram (ug) 0.000001 g (1 X 10-6 g)
nanogram (ng) 0.000000001 g (1 X 10-9 g)
Unit
Volume
kiloliter (kl)
1,000 l (1 X 103 l)
liter (l)
1l
milliliter (ml) 0.001 l (1 X 10-3 l), 1cm3
microliter (ul) 0.000001 l (1 X 10-6 l)
Notice in the table above that one milliliter (ml) equals one cubic centimeter (1 ml = 1 cc or cm3).
Metric Conversions
Exponents
The table below shows two different ways to write numbers. For example, a second way to write
the number 1,000 is 1 X 103.
100 = 1
100 = 1 X 102
1000 = 1 X 103
10,000 = 1 X 104
0.01 = 1 X 10-2 0.001 = 1 X 10-3
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Examples
256 = 2.56 X 102
3287 = 3.287 X 103
0.055 = 5.5 X 10-2 Decimal Point
Metric conversions are done by moving the decimal point. When converting a large unit such as
meters to a smaller unit such as millimeters, the decimal point is moved to the right. When
converting smaller units to larger units, the decimal point is moved to the left. You must subtract
the exponents in order to determine how many places to move the decimal point.
Examples
Convert 2.6 cm to um.
This problem is solved by subtracting the exponents. The exponent for cm is -2; the exponent for
um is -6. Subtract the two numbers: (-2 - (-6) = 4). Therefore, to convert 2.6 cm to um, you must
move the decimal point 4 places to the right. 2.6 cm = 26000
Convert 57 um to cm.
The exponent for um is -6. The exponent for cm is -2. You must subtract these two number to
determine how many places to move the decimal point. -6 - (-2) = -4. The negative sign indicates
that you must move the decimal point 4 places to the left. 57 cm = 0.0057
Laboratory Exercise
Copy and paste problems from each section below into a Word document to be turned in at the end
of the semester in a notebook with the rest of the online lab assignments. You will be given one
grade (out of 100 pts) for your lab notebook. Be sure to include your name, course: BIOL150 D1,
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Name of Assignment, and Date at the top of each assignment.
Do not use scientific notation (exponents) or fractions in your answers to the questions below. Write
all of the zeros.
Length
Measurement of Length
Measure the width of this page using a small plastic ruler. Record your measurement in 1)
millimeters, 2) centimeters, and 3) meters. Record your answers on the answer sheet.
Use a meter stick to measure the width of the laboratory table in 4) millimeters, 5) centimeters, and
6) meters.
7) Which unit of measurement (kilometer, meter, centimeter, millimeter, micrometer, or nanometer)
would be most appropriate for measuring the width of this room?
Conversions of Length
Perform the following conversions.
8) 1 m = _____ cm.
9) 1 cm = _____ m.
10) 3.57 mm = _____ um.
11) 452 cm = _____ mm.
12) 0.04 um = _____ mm
13) 37.6 nm = _____ mm
14) 52 nm = _____ um
15) 0.05 um = _____ nm.
16) 4.3 m = _____ um
17) 4206 mm = _____ cm
18) 0.046 mm = _____ nm
19) 4.8 cm = _____ um
Use the following information to perform the calculations below.
Metric to English: 1 meter = 39.372 inches = 3.281 feet
English to Metric: 1 inch = 0.0254 meters; 1 foot = 0.3048 meters
20) 8.53 inches = _____ m Round your answer to the nearest 0.001 m.
21) 12 feet, 3 inches = _____ m Round your answer to the nearest 0.01 m.
Weight
Measurement of Weight
The laboratory scale shown below has a sensitivity of 0.001 g. Due to its sensitivity, moving air
will cause it to fluctuate. The glass chamber surrounding the weighing pan prevents air currents
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from interfering with the weight.
The scale in the photograph below has a sensitivity of 0.01 g. The scale can be set to zero by
pressing the zero (tare) button on the lower left part of the scale.
Place a small beaker on the pan of the scale and zero it by pressing down on the zero (tare) button
located on the front of the scale. Place a penny in the beaker to obtain its weight.
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22) How much does the penny weigh in grams?
Remove the beaker from the scale and weigh the penny without using the beaker. You must first
zero the scale before weighing the penny.
Conversions of Weight
Perform the following conversions.
23) 37 g = _____ mg
24) 0.047 mg = _____ g
25) 45.36 g = _____ kg
Use the following information to perform the calculations below.
Metric to English: 1 g = 0.035274 ounces = 0.0022046 pounds
English to Metric: 1 ounce = 28.3495 grams; 1 pound = 453.59 grams
26) 150 pounds = _____ kg Round your answer to the nearest 0.01 kg.
27) 3 oz = _____ g Round your answer to the nearest 0.01 g.
Volume
Measurement of Volume
Obtain a 10 ml graduated cylinder (shown below) and fill it about half full with water.
28) Hold the graduated cylinder in a vertical position at eye level and read the number of milliliters
of water that are in the cylinder. Be sure to read the water at the bottom of the meniscus. The arrow
points to the bottom of the meniscus in the photograph below. What is the volume of water in the
cylinder?
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Use a 50 or 100 ml graduated cylinder to determine the amount of liquid that a test tube can hold
(it's volume).
29) How did you determine the volume of the test tube?
Conversions of Volume
30) 42 ml = _____ l
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31) 27 ul = _____ l
32) 3.6 l = _____ ml
33) 1 ml = _____ ul
Sometimes volume is measured using cubic centimeters (abbreviated cc or cm3). One cubic
centimeter equals one milliliter (1cc = 1ml).
34) 27 l = _____ cc (or cm3)
Use the following information to perform the calculations below.
Metric to English: 1 liter = 1.0567 quarts = 0.26217 gallons
English to Metric: 1 quart = 0.94635 liters; 1 gallon = 3.7854 liters
35) 2.3 quarts = _____ liters Round your answer to the nearest 0.01 liter.
36) 0.5 gallons = _____ liters Round your answer to the nearest 0.01 liter.
Temperature
Measurement of Temperature
The following temperature measurements should be done in Centigrade (Celsius):
37) Calculate the temperature of the air in the laboratory room if the thermometer reads 98°F.
38) Calculate the temperature of ice water if the thermometer reads 34°F.
39) Calculate the temperature of boiling water if the thermometer reads 212°F.
Conversions of Temperature
The temperature in Fahrenheit can be converted to Centigrade (Celsius) using the formula:
°C = 5/9(°F - 32)
For example, to convert 60° F to ° C, subtract 32 (=28), multiply it by 5 (=140) and divide it by 9
(=15.56).
The steps listed above are performed in reverse order to convert Centigrade to Fahrenheit. The
equation is below:
°F = (9/5 °C) + 32
For example, 20° C is converted to ° F by multiplying it by 9 (= 180), dividing it by 5 (= 36), and
adding 32 (=68).
40) 72° F = _____°C For this one, use the formula °C = 5/9(°F - 32). Round your answer to the
nearest 0.1.
(Note- If you do not have a calculator, use the one on the computer. Click Start, Programs,
Accessories, Calculator).
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41) 37° C = _____°F For this one, use the formula °F = ( 9/5 °C) + 32
What is DENSITY ?
Density = Mass/Volume
Density is an intensive property of matter that is defined as the ratio of an object's mass to its
volume. Mass is the amount of matter contained in an object and is commonly measured in units of
grams (g). Volume is the amount of space taken up by a quantity of matter and is commonly
expressed in cubic centimeters (cm3) or in milliliters (ml) (1cm3 = 1 ml). Therefore, common units
used to express density are grams per milliliters (g/ml) and grams per cubic centimeter (g/cm3).
Let's look at an example. A typical brick has a mass of 2,268 g and occupies a volume of 1,230
cm3. The density of the brick is therefore:
2,268 g/1,230 cm3 = 1.84 g/cm3
Density is an easy concept to confuse. For example, many items that we commonly think of as
"light" or "heavy" do not have different masses, but they do have different densities. Look at the
table below for examples of the densities of common substances.
Density of Some Common Substances
Substance
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Density (g/cm3)
Air
0.0013
Feathers
0.0025
Wood(Oak)
0.6 - 0.9
Ice
0.92
Water
1.00
Bricks
1.84
Aluminum
2.70
Steel
7.80
Silver
10.50
Gold
19.30
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Density Problems
42) What is the volume of a tank that can hold 18 754 Kg of methanol whose density is
0.788g/cm3?
43) What is the density of a board whose dimensions are 5.54 cm x 10.6 cm X 199 cm and
whose mass is 28.6 Kg?
45) CaCl2 is used as a de-icer on roads in the winter. It has a density of 2.50 g/cm3. What is the
mass of 15.0 L this substance?
46) Measure the length of a pencil in inches______________ and cm _____________________.
47) Measure the length of a TV remote control in inches________________ and cm
_________________.
48) Measure the length of a credit card or business card in inches ______________ and cm
______________.
49. Measure the diameter of a CD-Rom in inches ________________ and
cm____________________.
50. Measure the length of the width of a sheet of paper in inches ________________ and cm
_____________.
References and Credits
1. http://faculty.clintoncc.suny.edu/faculty/michael.gregory/files/Bio%20101/Bio%20101%20Laboratory/Metric% 20System/Metric_System.htm
2. http://www.visionlearning.com/library/module_viewer.php?mid=37
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