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Homework answers / question archive / Lab Topic 1 The Metric System Measurements and Laboratory Equipment Introduction One requirement of the scientific method is that results be repeatable
Lab Topic 1
The Metric System
Measurements and Laboratory Equipment
Introduction
One requirement of the scientific method is that results be repeatable. As numerical results are more precise than purely written descriptions, scientific observations are usually made as measurements. Of course, sometimes a written description without numbers is the most appropriate way to describe a result.
The Metric System
Logically, units in the ideal system of measurement should be easy to convert from one to another (for example, inches to feet or centimeters to meters) and from one related measurement to another (length to area, and area to volume). The metric system meets these requirements and is used by the majority of citizens and countries in the world. Universally, science educators and researchers prefer it. In most nonmetric countries, governments have launched programs to hasten the conversion to metrics. In fact, the U.S. Department of Defense adopted the metric system in 1957, and all cars made in the United States have metric components. As expected there has been some reluctance on the part of many Americans to change over – some reasons are economic (having to retool factories and households); normal resistance to change and probably some feeling that the metric system is foreign in more ways than one.
It is interesting to take some historical notice of how the metric system came into existence. Prior to the French revolution there was little international agreement on standard weights and measures. Each country had its own standards based on some transient things like the length of the king’s foot or middle knuckle. Just before the French revolution the French Academy of Sciences decided to work on a system of measures based on universal, scientific principles. They decided that the system should be based on a unit of length that was one ten millionth of the distance from the North Pole to the equator. That unit was called the meter. The revolutionists, when they came into power, agreed with the change because it represented a further repudiation of the old ways and another step towards “reason”. Napoleon gave several awards to the scientists and mathematicians who helped devise the new system (including one to Joseph Lagrange who was lucky not to be beheaded in the revolution due to his association with the monarchy). The advantage of metric measurements was quickly appreciated by scientists and others (including merchants, mechanics etc.) from other countries and it spread from France and was eventually adopted almost everywhere. In 1819 an English physicist and chemist, William Wollaston, argued against Britain’s adopting the system and as a result Britain and the commonwealth countries declined to convert to its use. Unfortunately, the United States followed Britain’s lead and also declined – we have been saddled with the irrational English system of weights and measures ever since (ironically the British and the other commonwealth countries have since converted but, alas, we are taking an inordinate amount of time to do so).
The metric reference units are the meter for length, the liter for volume, the gram for mass, and the degree Celsius for temperature. Regardless of the type of measurement, the same prefixes are used to designate the relationship of a unit to the reference unit. Table 1.1 lists the prefixes we will use in this and subsequent exercises. The metric system is a decimal system of measurement (based on ten (deci)). Metric units are 10, 100, 1000, and sometimes 1,000,000 or more times larger or smaller than the reference unit. Thus, it's relatively easy to convert from one measurement to another either by multiplying or dividing by 10 or a multiple of 10.
TABLE 1.1 Prefixes for Metric System Units
Prefix of Unit (Symbol) 
Part of Reference Unit 
nano (n) 
1/1,000,000,000 = 0.000000001 = 10^{9} 
micro (?) 
1/1,000,000 = 0.000001 = 10^{6} 
milli (m) 
1/1000 = 0.001 = 10^{3} 
centi (c) 
1/100 = 0.01 = 10^{2} 
kilo (k) 
1000 = 10^{3} 
There are additional prefixes, but these will suffice for now for our work in Biology. A prefix in front of a unit tells you how many of that unit you have. For example:
In this set of exercises, we examine the metric system and compare it to the American Standard system of measurement (feet, quarts, pounds, and so on).
MATERIALS
Per lab room:



? source of distilled water (dH_{2}0) 
? 
hot plate 
? metric bathroom scale 
? 
boiling chips 
? ice 
? 
thermometer on holder 
Per student group of twofour.
? 30cm ruler with metric and American (English) Standard units on opposite edges 

? 250ml beaker made of heatproof glass 
? 1gallon milk or water bottle 
? 250ml Erlenmeyer flask 
? metric tape measure 
? 3 graduated cylinders:10ml, 25ml, 100ml 
? 1l measuring cup 
? lquart jar or bottle marked with a fill line 
? nonmercury thermometer(s) with 
? onepiece plastic dropping pipette (not graduated) or Pasteur pipette and bulb 
Celsius (^{o}C) and Fahrenheit (^{o}F) scales (about 220110 ^{o}C) 
? graduated pipette and safety bulb or filling 
? a triple beam balance 
device
PROCEDURES
A. Length ( 15 min.)
Length is the measurement of a real or imaginary line extending from one point to another. The standard unit is the meter, and the most commonly used related units of length are
1000 millimeters (mm) = 1 meter (m)
100 centimeters (cm) = 1 m
1 kilometer (km) = 1000 m
For orientation purposes, the yolk of a chicken egg is about 3 cm in diameter. Since the difference between metric units is based on multiples of 10, it's fairly easy to convert a measurement in one unit to another. Before we do that, let’s review a few simple rule from mathematics: (note: “N” means any number).
Rule 1: 
Any number multiplied by one equals the original number and doesn’t change its value. That is: N x 1 = N 

For example: 6 x 1 = 6 

153 x 1 = 153 

½ x 1 = ½ 
Rule 2: 
Any number divided by itself equals one, or N/N = 1 

For example: 7/7 =1 

½ / ½ = 1 

x/x =1 
Rule 3: 
When multiplying units expressed as fractions, units cancel like numbers. 

For example: kg x cg x mg 

1 kg cg 

Here, the kg and cg cancel and we are left with mg, as follows: 

1 
Now we are ready to perform metric conversions. We will do this by multiplying the given value by one or more conversion factors to get the value in the desired units. Doing an example best shows this:
1a. Convert 8 km into m:
We know that 1 km = 1000 m. By dividing this equation by 1000 m, we get:

1 km 
= 1000 m 


1000 m 
1000 m 


or, 



1 km 
= 1 


1000 m 



This can also be written: 
1000 m = 
1 
1 km
Recall, multiplying by “1” does not change the value of the original number. Therefore, we can write:
8 km x 1000 m = 8 km x 1000 m = 8000 m
1 km 1 km
(Why did we use 1000m/1 km and not 1 km/1000m for our conversion factor?)
1b. Convert 6 cm into m:
We know that 1 m = 100 cm. By using the form of one, 100 cm / 1 m, we can multiply as follows:
6 cm x 1 m = 6 m 100 cm 100
Try the following: 
= 0.06 m 
a) 5 mm = ______m b) 5.5 m = ______ µm 
c) 9 km = _______nm 
(Hint: the last example requires two conversion factors.)
2. Measure the length of this page in centimeters to the nearest tenth of a centimeter with the metric edge of a ruler. Note that nine lines divide the space between each centimeter into 10 millimeters.
The page is _______________ cm long.
Calculate the length of this page in millimeters, meters and kilometers.
________________mm ______________m _____________ km
Now repeat the above measurement using the English side of the ruler. Measure the length of this page in inches.
______________in. Convert your answer to feet and then yards.
_________________ ft _____________ yds
Explain why it is much easier to convert units of length in the metric system than in the English
System _____________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
B. Volume (20 min.)
Volume is a measure of the space an object occupies. The metric standard unit of volume is the liter (l), and the most commonly used subunit, the milliliter (ml). There are 1000 ml in 1 liter. A chicken egg has a volume of about 60 ml.
The volume of a box is the length (l) x the width (w) x the height (h) (Figure A – 1).
The amount of water contained in a cube with sides 1 cm each in length is 1 cubic centimeter (cc)



Figure A 
 
2 

Relationship between the units of length, 
volume, and mass in the metric system. 


(1 
cm x 1 cm x 1 cm) which for all practical 
purposes equals 1 ml (Fig A 
 

2 
). 

1. 

How many milliliters are there in 1.7 l? 



___________________ml 


How many liters are there in 1.7 ml? 



____________________l 








V = l x w x h 


F 
igure A 
 

1 


Determining the volume 


of a box 
. 







Figure A  3 Apparati commonly used to measure volume: (a) pipette filling device, (b) pipette safety bulb,
(Photo by D. Morton and J. W. Perry.)
Figure A  4. Draw a meniscus in this plain cylinder. 

______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
TABLE A2 Estimate of the Number of Drops in 1 ml
Trial 

Drops/ml 
1 


2 


3 



Total 


Average 

C. Mass (25 min.)
Mass is the quantity of matter in a given object. The standard unit of mass is the kilogram (kg), and other commonly used units are the milligram (mg) and gram (g). There are 1,000,000 mg in 1 kg and 1000 g in 1 kg. A chicken egg has a mass of about 60 g. Note that the following discussion avoids the term weight. Mass is a constant (scalem). Your mass on the Earth is the same as your mass on the Moon. However, since gravity on the Moon is 1/6 of that on Earth, your weight on the Moon would be less. For example, a 60 lb. person on earth would weight 10 lbs. on the Moon, but that person would have the same mass. However for our purposes, we will use mass and weight interchangeably.
_______________________mg
Convert 1.7 g to milligrams and kilograms.
_______________________mg _________________ kg
Approximately how many liters are present in 1 cubic meter (m^{3}) of water? Since each of the sides of a cubic meter ( m^{3}) is 100 cm in length, it's easy to calculate the number of cubic centimeters (that is, 100 cm X 100 cm X 100 cm = 1,000,000 cc). Now just change cubic centimeters to milliliters and convert 1,000,000 ml to liters.
1,000,000 ml = _________ l
What is its mass in kilograms?______________________ kg.
Figure A 
 

5 

Triple Beam Balance 



movable masses 
10 
 
g graduations 


on the three beams 


100 
 
g graduations 


0 
. 1 
 
g and 1 
 
g 


pan graduations 



zero adjust knob 

balance marks 



TABLE A3 Weighing an Unknown Quantity of Water with a
Triple Beam Balance
Objects Masses (g)

Beaker and water

Beaker

Water

What is the volume?__________________ ml
4. Using the triple beam balance, determine the mass (that is, weight) of a brick of coffee in grams.
_______________________g
(1) Modified from C M Wynn and G. A. Joppich, Laboratory Experiments for Chemistry, A Basic Introduction, 3^{rd} ed. Wadsworth, 1984.
D. Estimating Length, Volume, and Mass (10 min.)
Now that you have experience using metric units, let's try estimating the measurements of some everyday items.
____________g
TABLE A4 Differences Between Estimates and Measurements
Number Estimate Measurement Estimate  Measurement 
1 cm cm cm 
2 m m m 
3 ml ml ml 
4 l l l 
5 g g g 
6 kg kg kg 
(How good are you at estimating?)
E. Temperature (About 20 min.)
The degree of hot or cold of an object is termed temperature. More specifically, it is the average kinetic energy of molecules. Heat always flows from high to low temperatures. This is why hot objects left at room temperature always cool to the surrounding or ambient temperature, while cold objects warm up. Consequently, to keep a heater hot and the inside of a refrigerator cold requires energy. Thermometers are instruments used to measure temperature.
ENGLISH SYSTEM
We in the United States are accustomed to the Fahrenheit scale to measure temperature. When you realize that Fahrenheit, over 200 years ago, created the lowest temperature he could (by mixing equal parts snow and salt) and called that temperature zero, it is easy to see why this scale is so far out of date. Water on Fahrenheit's scale freezes at 32? and boils at 212? advanced for his time, antiquated and almost silly for ours. This discourse is not a “put down” of Fahrenheit; to the contrary he was a very bright man who pioneered the use of mercury in thermometers because of its constant rate of expansion over temperature ranges. We are merely saying that our clinging to a cumbersome, irrational system based on 200 year old technology is unfortunate.
METRIC SYSTEM
Celsius took pure water at sea level and said it freezes at 0? and boils at 100? and he put 100 divisions between.
The Fahrenheit scale has 180 divisions between the freezing and boiling points of water (212 – 32) whereas Celsius has 100. Therefore, the Celsius degrees are almost twice as big as those of Fahrenheit. 180F to 100C = 1.8 to 1 = 9 to 5.
CAUTION: Do not touch the hot beaker, the boiling water, or the edges of the hot plate.
What temperature is 4^{o}C in degrees Fahrenheit? ________________^{o}F
What is body temperature, 98.6 ^{o}F, in degrees Celsius? ___________________^{o}C
^{o}F = 9/5 (^{o}C) + 32 ^{ o}C = 5/9 (^{o}F  32)
^{o}F ^{o}C water freezes 32 0 refrigerator temperature 41 5 room temperature 68 20 body temperature 98.6 37 water boils 212 100
Table A5 Comparison of Celsius and Fahrenheit Temperatures
Location ^{o}C ^{o} F 
Room 
Cold running tap water 
Hot running tap water 
Ice water 
Boiling water 
Lab Topic 1B_________________________________________________
Metric System Conversions: An Alternative M. Lakrim, Ph. D.
Activity 1: Conversion within the Metric System
To convert units to multiples or to fractions, use the following examples and table:
Example 1: Fractions (larger to smaller)
Convert 1 gram into milligrams (1 g = x mg) [See table below].
1st: Write the number "1" in the column "Units–gram"
2nd: Fill each column with zero "0" until you reach the desired column "milli"
3rd: Read the whole number and report it on your answer sheet
1 g = 1,000 mg
Example 2: Multiples (small to larger)
Convert 12.5 meters into kilometers (12.5 m = x km) [See table below].

1st: 
Write the number "12.5: on the column "Units–meter". Put only one figure at each column: "2" in column "Units–meter" "1" in column "deca" and "5" in column "deci: 

2nd: 
Fill the remaining columns up with zeroes until you reach the desired column "kilo" 

3rd: 
Read the whole number and report it on your answer sheet 


12.5 m = 0.0125 km 
Multiples 
Units 
Fractions 

kilo 
hecto 
deca 
gram, liter, meter 
deci 
centi 
milli 







1 
0 
0 
0 
0 
0 
1 
2 
5 


25
Exercise 1. Conversions
Using the table below, convert the following:

2 g = cg 

12 g = mg 

30 mg = g 

2 km = m 

3.5 km = m 

1 l = cl 

13.5 l = ml 

20 ml = l 

100 dl = l 
Multiples 
Units 
Fractions 



Kilo 
Hecto 
Deca 
Gram, Liter, Meter 
Deci 
Centi 
Milli 




































































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