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Units of Measurement Chapter 2

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Units of Measurement Chapter 2
Chapter 2
Units of Measurement
Measurement --- means determining the quantity of something.
How much do we have ?
A measurement is almost always determined by using a
measuring device, such as a scale for weight (mass), a
thermometer for temperature, etc.
We measure many things in everyday life, however, there are
5 major things that we measure in science.
• Length/Distance
• Volume
• Mass/Weight
• Temperature
• Time
There are 2 systems of measurement used in the world today.
The “British/U.S.” system.
This is the system with which we are familiar
because we learned it in this country and we use it every day.
For example, we often purchase 10 gallons of gasoline.
In the “British/U.S.” system, a gallon is a unit of VOLUME.
Outside of Great Britain and the United States, the rest of the
world uses the “Metric” system.
The “Metric” system is also the only system used in Science.
For that reason, learning the metric system is an important
part of the study of all sciences.
The “British/U.S.” system is totally arbitrary with no real
relationships between units.
For example, there are 12 inches in a foot
3 feet in one yard
and, 5,280 feet = one mile
The relationships between these units is totally arbitrary,
and not related to anything !
In the “Metric” system all units are based on multiples of 10,
100, 1000, etc., and is so indicated by the prefix.
The Metric System of Measurements
• For length/distance, the standard unit is the meter.
One kilometer (km) = 1000 meters (the prefix
“kilo” means 1000).
One centimeter = meter/100 (one
onehundredth of a meter)
One millimeter = meter/1000 (one
onethousandth of a meter
For volume, the standard unit in the
metric system is the liter.
• One milliliter (mL) = liter/1000
(one one-thousandth of a liter.)
And remember that mL = cm3 = cc
All three are used interchangeably in
science, especially in medicine
For mass (weight) the standard unit is
the gram.
A kilogram (kg) = 1000 grams.
A milligram (mg) = gram/1000
One one-thousandth of a gram.
The measurement of quantity can use different systems
•Length/Distance
Number of Systems
2 (Brit or metric)
• Volume
2
“
• Mass/Weight
2
“
• Temperature
3
• Time
1
Two important definitions with numbers:
Page 28 -29
A measured number is a number obtained by measuring
quantity with some sort of instrument.
For example, in order to measure the weight of a
patient, you need to use a scale.
In order to measure today’s temperature, you
need a thermometer.
An exact number is a number obtained either by counting
or by definition.
For example if a bag contains 3 doughnuts, you
obtain that number by counting, or if you were told that the
bag contained a dozen doughnuts, you know that, by
definition, a dozen means 12. Therefore that is also an
exact number.
Use Conversion Factors - - Page 38, Table #2.7
10
Problem Solving - - Page 41 - 45, Section #2.6
Page 45 Problem #2.55b:
A patient needs 0.024 grams of a sulfa drug. There are 8-mg
tablets in stock. How many tablets should be given ?
Solve by using the conversion factor: 1 gram = 1000 milligrams
Therefore, 0.024 grams X 1000 mg/gram = 24 milligrams
And, 24 mg/ 8mg per tablet = 3 tablets ANS
General Problem Solving
Find the density (in g/cm3) of a metal cube with a mass of
50.3 grams and an edge length of 2.65 cm.
Solve:
For a cube, Volume = (length)3
Therefore, V = (2.65)3
So, V= 18.61 cc
And, d = g/cc
d = 50.3/18.61 = 2.70 g/cc ANS
Page 45 Problem #2.54 d.
Blueberry high-fiber muffins contain 51% dietary fiber. If a package with a net weight
of 12 ounces contains 6 muffins, how many grams of fiber are in each muffin ?
Solution:
First, convert the weight of each muffin to grams: 12 oz./6 muffins = 2 oz. per muffin
Then, using the conversion factor (1 oz. = 28 g)
28 g/oz. X 2 oz./muffin = 56 grams per muffin.
Finally, 56 grams x 0.51 = 28.56 grams of fiber per muffin. (ANS.)
Problems on the Handout
A physician has prescribed a dosage of 50 mg of Nexium to
a patient every six hours. If you have only 25 mg tablets on
hand, how many tablets will be needed for 3 days ?
Solve:
• 50 mg per dosage divided by 25 mg per tablet =
2 tablets per dosage.
• 3 days (X 24) = 72 hours.
• 72/6 = 12 dosages.
• 12 dosages X 2 tablets/dosage = 24 tablets ANS
Density (Page 45)
The density of a substance is defined as the
ratio of its mass (weight) to its volume.
Therefore, the formula used to calculate density is d = m/v
The mass (weight) is almost always in grams and the volume is
almost always in mL (for milliliters) or cc or cm3 (for cubic
centimeters) Page 45, Section #2.7
Densities of Common Substances
Page 46 …….Table #2.9
16
Volume by Displacement
A solid
Page 47
• completely submerged
in water displaces its
own volume of water
• has a volume
calculated from the
volume difference
45.0 mL − 35.5 mL
= 9.5 mL
= 9.5 cm3
17
Specific Gravity (Page 48)
The specific gravity of a substance = its density divided by the
density of water, which is 1.0 g/mL
Therefore, specific gravity = density
AND, the two terms are interchangeable and have the
same meaning.
What is the density of a nugget of gold weighing 22.5 grams and
having a volume of 2.38 cc ?
Calculation:
d = 22.5 g/ 2.38 cc
d = 9.45 g/mL
See Page 49 (Problem #2.59c) for a density problem calculation
in which the volume is measured by water displacement.
Another example:
A marble weighing 35 grams is dropped into a beaker
containing 250 mL’s of water and the new water volume is 275
mL’s. What is the density of the marble?
Solve:
Volume of the marble = V2 - V1 (new volume minus the original volume)
V2 = 275 mL, and V1 = 250 mL therefore, the volume of the
marble = 275 – 250
= 25 mL
The density calculation is
d = 35 g/25 mL
d = 1.40 g/mL ANS
Practice problems: Page 49
Problems # 2.60 – 2.62
Another example:
Acetone (nail polish remover) has a density of 0.7857 g/cc.
What is the mass in grams of 28.56 mL of acetone ?
If d = 0.7857 , V = 28.56 mL and d = m/v,
then, m = d X V
Mass = density times volume
Hence:
mass = 0.7857 g/mL X 28.56 mL
mass = 22.44 grams ANS
An ibuprofen suspension for infants contains 100-mg/5.0 mL.
The recommended dose is 10 mg/ kg of body weight.
How many mL’s of this suspension should be given to an infant
weighing 18 pounds ?
Solve:
18 lbs = 18/2.2 lbs per kilo = 8.18 kg is the patient body wt.
Therefore, correct dosage is 8.18 kg X 10 mg per kg = 81.8 mg
And, (81.8/100) X 5.0 = 4.09 mL ANS
Practice Problems for Chapter 2:
Page 45 #2.52 & #2.53
Page 52 #2.78 through #2.83
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