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/cm 3 ) 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 cm 3 (for cubic centimeters) Page 45, Section #2.7
Densities of Common Substances Page 46.Table #2.9 16
Volume by Displacement A solid 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 cm 3 Page 47 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 = V 2 - V 1 (new volume minus the original volume) V 2 = 275 ml, and V 1 = 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