1.05 Units and the Metric System 1 1.05 Units and the Metric System 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. 2 1.05 Units and the Metric System
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 3 1.05 Units and the Metric System System of Measurements 4 1.05 Units and the Metric System
Units - These give meaning to the measurement Rest of the World uses the metric system. 5 1.05 Units and the Metric System 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 6 1.05 Units and the Metric System
There are seven quantities in which all units can be derived; these are the base units and the SI defines these as: Quantity Unit Symbol length meter m mass kilogram kg time seconds s temperature kelvin K amount mole mol electric current ampere A luminous intensity candela cd All others units are derived units 7 1.05 Units and the Metric System Derived units result from these seven base units. i.e., vol. (L) derived from m 3 meters. energy (J) derived from N m or (kg m / s 2 ) m pressure (psi) derived from lb. /in 2 or (kg /m 2 ) 8 1.05 Units and the Metric System
The SI units employ a series of prefix to indicate decimal fraction or multiple of units. Prefix Symbol exp factor factor Mega M 10 6 1,000,000 kilo k 10 3 1,000 deci d 10-1 1 / 10 centi c 10-2 1 / 100 milli m 10-3 1 / 1,000 micro m 10-6 1 /1,000,000 nano n 10-9 1 / 1,000,000,000 pico p 10-12 1 / 1,000,000,000,000 9 1.05 Units and the Metric System Consider the relationship between each metric prefix. Prefix Fraction Decimal Exponential Conversion Tera 1 000 000 000 000 1 000 000 000 000 1 e12 1 000 000 000 000 m = 1 Tm Giga 1 000 000 000 1 000 000 000 1 e9 1 000 000 000 m = 1 Gm Mega 1 000 000 1000 000 1 e6 1 000 000 m = 1 Mm kilo 1000 1000 1 e3 1 000 m = 1km - 1 1 1 1m = 1m deci 1/10 0.1 1 e-1 1m = 10 dm centi 1 / 100 0.01 1 e-2 1m = 100 cm milli 1 / 1000 0.001 1 e-3 1m = 1000 m micro 1/1 000 000.000 00 1 1 e-6 1m = 1 000 000 m nano 1/1 000 000 000.000 000 000 1 1 e-9 1m = 1 000 000 000 m pico 1/1 000 000 000 000.000 000 000 000 1 1 e-12 1m = 1 000 000 000 000 m femto 1/1 000 000 000 000 000.000 000 000 000 000 1 1 e-15 1m = 1 000 000 000 000 000 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 (mg) and grams (g) is either 1g = 1 10-6 mg or 1,000,000 mg = 1g. It is easier to use the 1,000,000 mg = 1g conversion since this conversion does not involve negative exponents. 10 1.05 Units and the Metric System
In the English system, exact conversion factors must be known. i.e., How many inches in a marathon (26 miles)? To solve this, must know that there are 63,360 in = 1 mile Mile Yard feet 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 Therefore in a marathon there are : 26 mile 63, 360 in = 1, 647, 360 in 1 mile 11 1.05 Units and the 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 meters 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 = 1 10 7 cm 12 1.05 Units and the 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, 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. 13 1.05 Units and the Metric System 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 = 1 10 9 nm 1 in = 2.54 cm 1 mi. = 1.609 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 1 gal = 3.785 L 1 fl oz = 29.57 ml Mass - quantity of matter English 1 lb. = 16 oz 1 Ton = 2000 lb. Metric 1 kg = 1000 g 1 g = 1000 mg 1 lb. = 453.6 g 1 kg = 2.205 lb. 14 1.05 Units and the Metric System
Order of magnitude as expressed via metric measurements 15 1.05 Units and the Metric System 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 miles - km Volume gallons - Liters Mass pounds - kg Distance of one light year Volume of space 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. Water of water in great lakes Mass of Statue of Liberty. 1000 mi km volume of water in Shamu's pool Mass of average elephant. 500 mi km volume of water in Miramar's pool 1 ton g kg 100 mi km Volume of gasoline in Hummer 300 lb 60 mi km Volume of water in 21 gallon tank 150 lb 25-mi km volume of air in lungs 100 lb 10 mi km volume in 1 gallon 50 lb 16 1.05 Units and the Metric System
Prefix Fraction Decimal Exponential Conversion Tera 1 000 000 000 000 1 000 000 000 000 1 e12 1 000 000 000 000 m = 1 Tm Giga 1 000 000 000 1 000 000 000 1 e9 1 000 000 000 m = 1 Gm Mega 1 000 000 1000 000 1 e6 1 000 000 m = 1 Mm kilo 1000 1000 1 e3 1 000 m = 1km - 1 1 1 1m = 1m deci 1/10 0.1 1 e-1 1m = 10 dm centi 1 / 100 0.01 1 e-2 1m = 100 cm milli 1 / 1000 0.001 1 e-3 1m = 1000 m micro 1/1 000 000.000 00 1 1 e-6 1m = 1 000 000 m nano 1/1 000 000 000.000 000 000 1 1 e-9 1m = 1 000 000 000 m pico 1/1 000 000 000 000.000 000 000 000 1 1 e-12 1m = 1 000 000 000 000 m femto 1/1 000 000 000 000 000.000 000 000 000 000 1 1 e-15 1m = 1 000 000 000 000 000 m 17 1.05 Units and the Metric System