2.02 Units and the Metric System

Transcription

1 2.02 Units and the Metric System Dr. Fred Omega Garces Chemistry 100 Miramar College Units and the Metric System

2 Measurements In our daily lives we deal with making measurement routinely. i.e., How much gasoline is required to fill your gas tank? What time did you wake up this morning? How fast did you drive to school today? Doctors, nurses, pharmacist- Doctors and nurses make measurement constantly. Measurements like pulse rate, blood pressure, temperature, drug dosage. Math - The language of Science Scientist make countless measurement during their experiment to prove or disprove theory Units and the Metric System

3 Numbers without meaning What is your response if I told you that I weigh 64.4 You would either think I was mad or anorexic. In any measurement Magnitude (the number) as well as Unit (meaning) must be stated. Otherwise it is Meaningless Units and the Metric System

4 System of Measurements What units are used? America The Rest of the World Scientific Community English System 1 ft = 12 in 1 yd= 3 ft 1 mi. = 1,760 Yd 1 mi = 5280 ft Metric System 1 km = 1000 m 1 m = 100 cm 1 m = nm Le System International d Unites time g sec length g m mass g kg temperature g Kelvin Units and the Metric System

5 Units gives meaning to the measurement What are Units? Standards used for quantitative comparison. i.e., Ft, mi, in, cm, mi/hr, km/min, gal, J, cal The U.S. prefers the English Unit system. Rest of the World uses the metric system Units and the Metric System

6 Metric system and the Le Systeme International d'unites (SI) The Metric system is convenient because it uses only one fundamental unit for each type of measurement, and all of its conversion factors are multiples of 10. The scientific community uses an updated metric plan called the SI units. SI (Le Systeme International d'unites) There are seven (7) quantities in which all units can be derived, this is the basis of the SI units; all other units are derived from these seven Units and the Metric System

7 SI units There are seven quantities (fundamental) in which all units can be derived; these are the base units and the SI defines these as: All others units are derived units Units and the Metric System

8 Relationship of SI to SI Derived Units Relationships of the SI units to SI derived units with special names Units and the Metric System

9 What are Derived Units? Derived units result from these seven base units. i.e., vol. (L) derived from m 3 g meters. energy (J) derived from N m or (kg m / s 2 ) m pressure (psi) derived from lb. /in 2 or (kg /m 2 ) Units and the Metric System

10 Ease of conversion of the SI units The SI units employ a series of prefix to indicate decimal fraction or multiple of units. Prefix Symbol exp factor factor Mega M ,000,000 kilo k ,000 deci d / 10 centi c / 100 milli m / 1,000 micro m /1,000,000 nano n / 1,000,000,000 pico p / 1,000,000,000, Units and the Metric System

11 Metric Prefix Relationship Consider the relationship between each metric prefix. Prefix Fraction Decimal Exponential Conversion Tera e m = 1 Tm Giga e m = 1 Gm Mega e m = 1 Mm kilo e m = 1km m = 1m deci 1/ e-1 1m = 10 dm centi 1 / e-2 1m = 100 cm milli 1 / e-3 1m = 1000 m micro 1/ e-6 1m = m nano 1/ e-9 1m = m pico 1/ e-12 1m = m femto 1/ e-15 1m = m In using the metric system conversion factor in dimensional analysis remember to use the conversion ratio that makes sense. For example the conversion between micrograms (µg) and grams (g) is either 1 µg = g or 1,000,000 µg = 1g. It is easier to use the 1,000,000 µg = 1g conversion since this conversion does not involve negative exponents Units and the Metric System

12 Conversion within English System In the English system, exact conversion factors must be known. i.e., How many inches in a marathon (26 miles 385 yards)? To solve this, must know that there are 63,360 in = 1 mile Mile n Yard n feet n inches To solve this problem the relationship between miles and in must be known. In fact to convert between miles, yards, feet and inches each relationship (conversion factor) must be known. Length 1 Mi. = 1,760 yd = 5,280 ft = 63,360 in 1 yards = 3 ft = 36 in Therefore in 26 miles, there are : 26 mile 63,360 in 1 mile = 1,647,360 = 1.6 million inches Units and the Metric System

13 Conversion within Metric System. Advantage of the metric system is that converting from one unit to the other is just a matter of multiplying or dividing by 10's. i.e., How many centimeters in a 100 km? To solve this, simply need to know that kilo means 1000, therefore there are 1000m = 1 km (conversion factor) and that there are 100 cm = 1 m Kilometers n meters n centimeters This is very useful in science, especially when you have to work numerical problems. Length 1 km = 1000 m, 1 m = 100 cm Therefore 100 km is equal to: 100 km 1000 m 1 km 100 cm 1 m = cm Units and the Metric System

14 English and Metric System. In science, measurement is based on the metric system (SI). Life in America is a bit more complicated because we live in a global world that uses the metric system but at home we use the English system. The metric system (or SI) is very useful in science, especially when you have to work numerical problems. When dealing with the metric system the conversion is easy. When dealing with English and metric, the conversion factor between two units must be known: i.e., 1 inch = 2.54 cm In the automotive industry, the U.S. still uses predominately the English system. If you want a wrench for example that is the next size smaller than a 7/16 -inch, it would be logical to use 6/16-inch. The correct next lower size is actually labeled 6/16-inch. It becomes really complicated if you are looking for the next smaller size for 3/4-inch because it is not 2/4 (or 1/2-inch) it is actually 11/16-inch -go figure Units and the Metric System

15 Other Metric relationship. Length - distance English 1 ft = 12 in 1 yd= 3 ft 1 mi. = 1,760 yd. Metric 1 km = 1000 m 1 m = 100 cm 1 m = nm English - Metric 1 in = 2.54 cm 1 mi. = km Volume - space English 1 gal = 4 qt 1 qt = 2 pt 1pt = 16 fl oz. Metric 1 L = 1000 ml 1 ml = 1 cm 3 = 1 cc English - Metric 1 gal = L 1 fl oz = ml Mass - quantity of matter English 1 lb. = 16 oz 1 Ton = 2000 lb. Metric 1 kg = 1000 g 1 g = 1000 mg English - Metric 1 lb. = g 1 kg = lb Units and the Metric System

16 Some interesting measurements Order of magnitude as expressed via metric measurements Units and the Metric System

17 Putting it in perspective In class you will be assigned a conversion project. It will be up to you to make the appropriate conversion. Be prepared to make a presentation on this assignment. You can create a poster, a PowerPoint slide show or come up with something creative. Length English - Metric miles - km Volume English - Metric gallons - Liters Mass English - Metric pounds - kg Distance of one light year Volume of space in universe Mass of universe Distance around the world. Volume of the sun Mass of sun, Jupiter, Earth, Moon Distance San Diego to NY City. Volume of earth Mass of water in ocean Distance SD to LA. Volume of water in ocean Mass of Empire State Building. Distance Pet Co to Qualcomm. Volume of water in great lakes Mass of Statue of Liberty mi to km volume of water in Shamu's pool Mass of average elephant. 500 mi to km volume of water in Miramar's pool 1 ton g kg 100 mi to km Volume of gasoline in Hummer 300 lb 60 mi to km Volume of water in 21 gallon tank 150 lb 25-mi to km volume of air in lungs 100 lb 10 mi to km volume in 1 gallon 50 lb Units and the Metric System

18 Summary Measurement - Measurement Consist of a Magnitude (a number) and a Unit (the meaning) Unit system - Le Systeme International d'unites ( SI ) There are three unit systems. The English, Metric and SI (Le Systeme International d'unites). The SI is derived from the metric and is more specific. The Metric system is based on prefixes which relates the magnitude of a number to another by factors of 10. Prefix Fraction Decimal Exponential Conversion Tera e m = 1 Tm Giga e m = 1 Gm Mega e m = 1 Mm kilo e m = 1km m = 1m deci 1/ e-1 1m = 10 dm centi 1 / e-2 1m = 100 cm milli 1 / e-3 1m = 1000 m micro 1/ e-6 1m = m nano 1/ e-9 1m = m pico 1/ e-12 1m = m femto 1/ e-15 1m = m Units and the Metric System

19 Sample Questions 1. Which one of the following measurements contains four significant figures? a) g b) g c) g d) e4 g 2. Which of the following has three (3) significant figures: a) 0.06 b) 1600 c) 1.090e3 d) One edge of a cube is measured and found to be 2.54 cm. What is the volume of the cube in in 3. (1.00 in = 2.54 cm) a) 16.4 b) 1.00 c) 106 d) How many centimeters are there in 1 kilometer? a) 100 b) 1e-5 c) 1000 d) 1e6 5. At what temperature does K = C a) 100 b) 0 c) 273 d) Never the same 6. The prescribed injection of a drug is oz. If the syringe is graduated in cubic centimeters, to what mark would you draw the drug? (29.6 ml = 1 oz) a) 5.00cc b) 0.34 cc c) cc d) 10.0 cc 7. Which of the following is the largest mass? a) 41 g b) 8.2e6 mg c) 3e3 mg d) 4.1e-8 Kg 8. Which is the fastest speed? a) 100 km/hr b) 100 mi/hr c) 1e5 m/hr d) 5.2e6 ft/hr Units and the Metric System

20 Sample Questions 9. The lethal dose of heroine is 150 mg per kilogram of body weight. Estimate how many grams of heroin would be lethal for a 200-lb man. a) 13.6 g b) 13.6 mg c) 13.6 oz d).0136 lb 10. You obtain the number on a calculator. If this number actually has four (4) significant figures, how should it be written? a) 1251 b) c) 1.250e3 d) 1.250e You obtain the number on a calculator. If you need to round this number to the hundredths, how should it be written? a) 1200 b) 250 c) d) How many of the following numbers have 5 significant figures: e a) 1 b) 2 c) 3 d) The number 6.33e-2 equals : a) b) c) 633. d) When expressed in exponential notation, the number becomes: a) 3.02e-4 b) 3.02e4 c) 3.02e3 d) 3.02e A woman who weights 38.5 Kg is most likely to be which of the following? a) a basketball center b) a discus thrower c) a gymnast d) a volleyball player 16. Which of the following is the shortest length? a) 1.21m b) 75 in c) 3 ft - 5 in d) a yard stick Units and the Metric System