Lab 1: Units and Conversions

Transcription

1 Lab 1: Units and Conversions The Metric System In order to measure the properties of matter, it is necessary to have a measuring system and within that system, it is necessary to define some standard dimensions, such as the foot, as a standard unit of length. There are two major measurement systems used around the world today -- the English or British system and the metric system, also known today as the International System (SI) of Units because it has established a standard set of measurements used by most of the nations of the world. In this class, we will be using mostly the SI system, since that is the international standard. The metric system is a decimal system of units. This means that larger and smaller units are some multiple of ten multiplied by the standard units. Prefixes are used to define these larger and smaller multiples as the following table shows: Prefix Fraction Decimal Power of Giga (G) 1,000,000,000 1,000,000,000 1 x 9 Mega (M) 1,000,000 1,000,000 1 x 6 Kilo (k) 1,000 1,000 1 x 3 Deci (d) 1/.1 1 x -1 Centi (c) 1/ x -2 Milli (m) 1/1, x -3 Micro (μ) 1/1,000, x -6 Nano (n) 1/1,000,000, x -9 Pico (p) 1/1,000,000,000, x -12 For example, one thousand meters is a kilometer (km), one hundredth of a meter is a centimeter (cm), and one thousandth of a second is a millisecond (ms). Conversions Converting Units It is often necessary to convert units from one system to another. For example, how many kilometers are there in miles, or how many inches in 20 centimeters? Making conversions is easy if you follow this procedure:

2 Example #1: mi. = km. 1. Find the conversions between miles and kilometers. If we look in a table, we find that 1 km.= mi. 2. Multiply mi. by the number of kilometers per mile: 1km mi mi 3. Collect numerical values and units together : 1 mi km mi 4. Perform the numerical calculation and cancel units to obtain: 5. Thus, Example #2: 16.1km mi km Convert 60 mph to m/s 1. Convert to meters per hour (canceling like units): mi 16m m h 1mi h 2. Convert above result to meters per second: m 1h 1min m h 60min 60s s Powers of or Scientific Notation Some numbers in science are very large or very small and can be written in a shortened version called scientific notation. For example, the mean distance from the Earth to the sun is 93,000,000 miles. This can be written as follows in all of the following ways: 93 x 1,000, x x x x x x 93 x x x 7.93 x 8 All are correct, but scientists generally express the number as a number with one nonzero digit in front of the decimal which is then multiplied by the correct power of. In this case, we would choose 9.3 * 7.

3 Engineers and medical professionals usually use what is called Engineering Notation. Engineering notation is similar to scientific notation, but the exponent is always a multiple of 3. The advantage of using engineering notation is that it allows the use of prefixes. For example, baby aspirin tablets usually contain.081 grams of aspririn. In scientific notation, this would be 8.1 x -2 grams, but in engineering notation, it would be 81 x -3 grams, or 81 milligrams. Very small numbers can be expressed by using a negative exponent (this is the same as dividing by ). The mass, g can be written in engineering notation by moving the decimal point behind the four, six places to the right. Thus the number can be written as: 34 x -6 (34 micrograms or 34 μg) Another advantage of scientific notation is the ease of working with very large and very small numbers when multiplying and dividing. In multiplication, the decimal parts of the numbers are multiplied together and the exponents are added together. Examples: Percent Error and Percent Difference Measurements always contain a certain degree of error. When a measured value is to be compared to an accepted (known true) value for the quantity in question, the percentage error is used: % error = [(Measured value Accepted Value)/(Accepted Value)] x 0 Notice that, if the measured value is larger than the accepted value, the % error will be positive. It the measured value is smaller than the accepted value, the % error will be negative. When we don t have a known correct (accepted) value, we can compare the results of two different measurements by calculating the percent difference is used: % difference = (Value 1 Value 2)/(Value 1 + Value 2) x 200

4 CONVERSION FACTORS BASIC WEIGHTS AND MEASURES ABBREVIATIONS inch foot yard mile ounce pound miles per hour Fahrenheit pint quart gallon centimeter meter kilometer gram kilometers per hour liter Celsius square cubic cubic centimeter LENGTH (Linear Measure) = in. = ft. = yd. = mi. = oz. lb. = mph = F = pt. = qt. = gal. = cm = m = km = gm = km/h = l = C = sq. = cu = cc 1 centimeter inches 1 meter = yards = feet = inches 1 kilometer = mile AREA (Square Measure) 1 sq inch = sq cm 1 sq foot = sq cm = sq m 1 sq yard = sq cm = sq m 1 acre = sq m 1 sq mile = 2.59 sq km = 640 acres 1 sq centimeter = sq in 1 sq meter =.76 sq ft = sq yd 1 sq kilometer = sq mi VOLUME (Cubic Measure) 1 inch = 2.54 centimeters 1 foot = centimeters 1 yard = meters 1 fathom = meters 1 rod = decameter 1 furlong = 40 rods 1 statute mile = kilometers 1 nautical mile = kilometers 1 cu inch = cu cm 1 cu foot = cu m 1 cu yard = cu m 1 cu centimeter = cu in 1 cu meter = cu yd LIQUID VOLUME LENGTH (Linear Measure)

5 1 ounce = ml 1 cup = l 1 pint = l 1 quart = l 1 gallon = l 1 liter = cups = pt. = qt. = gal. MASS (Avoirdupois Weight) 1 tablespoon = 15 ml 8.81 liters = 1 peck 1 liter = 1.06 qt. 1 ml = 1 cc TEMPERATURE EQUATIONS C = ( 5 / 9 )( F - 32 ) F = ( 9 / 5 )C + 32 K = C Freezing at Sea Level: 32 o F or 0 o C Boiling at Sea Level: 212 o F or 0 o C 1 ounce = gm 1 pound = kg = gm 1 ton = metric ton 1 gram = oz. 1 kilogram = oz. = lb. ADDITIONAL CONVERSIONS 31.5 gallons = 1 barrel 2 pints = 1 qt. 231 cu inches = 1 standard gal 4 quarts = 1 gal. 128 cu feet = 1 cord 16 ounces = 1 lb. = 1 pt pounds = 1 short ton 2240 pounds = 1 Long ton 1 fathom = 6 ft. ADDITIONAL CONVERSIONS 1 nautical mi. = km 8 quarts = 1 peck 1 teaspoon = 5 ml 4 pecks = 1 bushel

6 Units And Conversions Work Sheet I. Conversions Do the following conversions and put the answers in the blanks to the right. Show your work in the space below the problem inches = cm liters = qt m = mm kg. = lb kg. = gm megatons = tons ft. = m μsec. = sec. 8.

7 cm. = ft mm. = μm Gal/min = liter/s mi/h = m/s μg = mg MPH = m/s sec = years 15. II. EXPRESS IN SCIENTIFIC AND ENGINEERING NOTATION

8 III. EXPRESS IN NORMAL DECIMAL FORM x x IV. PERCENT ERROR AND PERCENT DIFFERENCE 21. Find the percent error between a measured 21. value of 47 gm and a true value of 50 gm. 22. Find the percent difference between two measured 22. values, 45.2 cm and 44.7 cm IV. SIGNIFICANT FIGURES All numerical answers resulting from a calculation should be written in decimal form and rounded to three significant figures. (Note that leading zeros in numbers less than 1 are not significant figures ) Examples: