THE INTERNATIONAL SYSTEM OF UNITS = THE METRIC SYSTEM. R. Ashby Duplication by permission only.

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1 CH 11 TOPIC 35 THE METRIC SYSTEM & FACTOR CONVERSIONS 1 You have mastered this topic when you can: 1) use SI units and their accepted alternatives in chemistry. 2) correctly determine the unit of a derived quantity. THE INTERNATIONAL SYSTEM OF UNITS = THE METRIC SYSTEM I) In order to simplify sharing quantitative measures, all scientists record them using the International System of Units = SI units. The most common quantities used in Chemistry and their SI units are listed in TABLE 1. TABLE 1: Most commonly used SI Units Quantity SI name SI unit length (distance) metre m mass gram g volume litre L time second s amount of substance mole mol A) A single quantity may be written using several different units. Study these examples. 1) e.g. A typical can of soda pop has a volume of 341 ml. This volume may be written as L because 341 ml is the same volume as L. The unit ml is used because it is more practical. 2) e.g. A typical car has a mass of approximately 1500 kg. This mass could be written as g because kg is the same mass as g. The unit kg is used because it is more practical. 3) Here is a list of alternate SI units commonly used in chemistry. TABLE 2: SI Units Unit Name Unit Symbol Distance Volume Mass Relative size giga G Gm GL Gg LARGE mega M Mm ML Mg kilo k km kl kg hecto h hm hl hg deka da dam dal dag g, L, m, etc. g, L, m, etc. m L g deci d dm dl dg centi c cm cl cg milli m mm ml mg micro µ µm µl µg nano n nm nl ng pico p pm pl pg small a) The units in TABLE 2 represent different sizes: small units LARGE units 1 pm < 1 µm < 1 mm < 1 cm < 1 dm < 1 m < 1 dam < 1 hm < 1 km < 1 Mm < 1 Gm

2 CH 11 TOPIC 35 THE METRIC SYSTEM & FACTOR CONVERSIONS 2 II) CONVERTING SI UNITS: ALL SI UNITS ARE BASED MULTIPLES OF 10 TABLE 3: Multiples of 10 relationships between SI Units Relationship mass volume distance G Gg = Mg 1 GL = ML 1 Gm = Mm M Mg = kg 1 ML = kl 1 Mm = km k 10 1 kg = 10 hg 1 kl = 10 hl 1 km = 10 hm h 10 1 hg = 10 dag 1 hl = 10 dal 1 hm = 10 dam da 10 1 dag = 10 g 1 dal = 10 L 1 dam = 10 m g, m, L 10 1 g = 10 dg 1 L = 10 dl 1 m = 10 dm d 10 1 dg = 10 cg 1 dl = 10 cl 1 dm = 10 cm c 10 1 cg = 10 mg 1 cl = 10 ml 1 cm = 10 mm m mg = µg 1 ml = µl 1 mm = µm µ µg = ng 1 µl = nl 1 µm = nm n ng = pg 1 nl = pl 1 nm = pm p A) A CONVERSION FACTOR is a fraction that represents an equal relationship between two SI units. e.g. Relationship Conversion Factor 12 dimes = 1 dozen dimes 12 dimes or 1 dozen dimes 1 dozen dimes 12 dimes 1 couple = 2 people 1 couple or 2 people 2 people 1 couple 1) 12 dimes represents the same amount as 1 dozen dimes and when it is written as the conversion factor, 12 dimes or 1 dozen dimes, which is a fraction representing the number 1. 1 dozen dimes 12 dimes 2) The relationships given in TABLE 3 above are used to create conversion factors. These patterns are used to create SI conversion factors. small number BIG UNIT BIG NUMBER small unit BIG NUMBER small unit small number BIG UNIT 1 Mg kg kg 1 Mg

3 CH 11 TOPIC 35 THE METRIC SYSTEM & FACTOR CONVERSIONS 3 3) Sample Problems 1: Write conversion factors describing the relationship between these SI units. 1. m and dm 1 m or 10 dm 10 dm 1 m 2. ml and cl 1 cl or 10 ml 10 ml 1 cl 3. Mg and kg 1 Mg or kg kg 1 Mg 4. ng and pg 1 ng or pg pg 1 ng 4) Required Practice 1: Write conversion factors describing these SI unit relationships. {Answers are on page 4 of these notes.} 1. GL and ML 2. dag and g 3. km and hm 4. nm and µm 5. dl and cl 6. dg and g III) CONVERTING SI UNITS TO AN ALTERNATE FORM A) SI units are converted by multiplying 1 or more conversion factors. The initial units are converted by starting with the known quantity then multiplying by the appropriate conversion factors having the unit we want in the numerator (top) and the unit we want to change, the initial units, in the denominator (bottom) so they cancel leaving the units wanted. 1) Sample Problems 2 1. How many ml are equal to 29.3 cl? 29.3 cl 10 ml 1 cl = 293 ml 29.3 cl = 293 ml 2. Convert kg to Mg kg 1 Mg 1000 kg = Mg kg = Mg 3. How many nm is equal to pm? pm 1 nm 1000 pm = nm pm = nm 2) Required Practice 2: Complete these conversions. {Answers are on page 4 of these notes.} hl =? dal mg =? cg dm = m Mm =? km µm =? mm 6. 2 pm =? nm B) MEMORIZE THESE CONVERSION FACTORS To convert between grams and milligrams: To convert between grams and kilograms: 1 g 1000 mg or 1000 mg 1 g 1 kg 1000 g or 1000 g 1 kg To convert between liters and millilitres: 1 L or 1000 ml 1000 ml 1 L

4 CH 11 TOPIC 35 THE METRIC SYSTEM & FACTOR CONVERSIONS 4 1) Sample Problems 3 1. How many mg are equal to 2.87 g? 2.87 g 1000 mg 1 g = mg 2. How many kg are equal to 85 g? 85 g 1 kg 1000 g = kg 2) Required Practice 3: Complete these conversions. {Answers are on page 5 of these notes.} g =? kg mg =? g kg =? g kg =? g L =? kl kl =? L C) METRIC CONVERSIONS INVOLVING MORE THAN ONE CONVERSION FACTOR 1) Sample Problems 4 1. How many mg are equal to 2.87 g? 2.87 g 10 dg 1 g 10 cg 1 dg 10 mg 1 cg = mg 2.87 g = mg 2. Convert dl to kl dl 1 L 10 dl 1 dal 10 L 1 hl 10 dal 1 kl 10 hl = kl dl = kl 3. Convert nm to dm nm 1 µm nm 1 mm µm 1 cm 10 mm 1 dm 10 cm = dm nm = dm 2) Required Practice 4: Complete these conversions. {Answers are on page 5 of these notes.} hm =? m cg =? µg µm =? m dal =? kl m =? Mm µg =? kg Required Practice 1 from page 3 ANSWERS TO THE REQUIRED PRACTICE 1. 1 GL or ML nm or 1 µm ML 1 GL 1 µm nm 2. 1 dag or 10 g 5. 1 dl or 10 cl 10 g 1 dag 10 cl 1 dl 3. 1 km or 10 hm dg or 1 g 10 hm 1 km 1 g 10 dg Required Practice 2 from page hl = 386 dal mg = cg dm = m Mm = km µm = mm 6. 2 pm = nm

5 CH 11 TOPIC 35 THE METRIC SYSTEM & FACTOR CONVERSIONS 5 Required Practice 3 from page kg g = x 10 2 g g = 5.14 x 10 4 g g kl L Required Practice 4 from page hm = 2130 m cg = 562 µg µm = m dal = kl m = Mm µg = kg BE SURE YOU PREPARE FOR MEMORY CHALLENGE-5 ON T28 T35!!

6 CH 11 TOPIC 35 THE METRIC SYSTEM & FACTOR CONVERSIONS 6 ASSIGNMENT At the top of your assignment, please print T35 The Metric System & Factor Conversions, your LAST then First name, block and date. Show all your work for questions requiring calculations; marks will not be awarded for final answers only. Complete these questions in the order given here. [Marks indicated in italicized brackets.] 1. Complete these metric conversions. SHOW THE CONVERSION FACTORS!! [18] a. 57 kg =? g b. 37 g =? mg c. 4.7 kg =? g d g =? kg e µg =? g f. 35 cm =? pm WHEN BALANCING EQUATIONS EVERY FORMULA MUST HAVE A COEFFICIENT 2. Balance and classify these equations. [14] a. NaCl (s) Na (s) + Cl 2(g) d. AlCl 3(aq) + NaOH (aq) Al(OH) 3(s) + NaCl (aq) b. Na (s) + O 2(g) Na 2 O (s) e. Al (s) + H 2 SO 4(aq) H 2(g) + Al 2 (SO 4 ) 3(aq) c. Na (s) + H 2 O (l) H 2(g) + NaOH (aq) f. C 8 H 18(l) + O 2(g) CO 2(g) + H 2 O (g) [22 marks in total] BE SURE YOU PREPARE FOR MEMORY CHALLENGE-5 ON T28 T35!!