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International System of Measurements Notes Chapter 2: Measurements and Calculations Scientific Notation It is used to easily and simply write very large numbers, and very small numbers. It begins with a number greater than zero & less than 10. In other words, one digit before the decimal point. This number is multiplied by an appropriate power of 10 Powers of 10 – positive exponents 0 5 10 = 1 10 = 100,000 1 6 10 = 10 10 = 1,000,000 2 7 10 = 100 10 = 10,000,000 3 8 10 = 1,000 10 = 100,000,000 4 9 10 = 10,000 10 = 1,000,000,000 Scientific notation of numbers greater than 1 2 136 = 1.36 x 10 4 15,000 = 1.5 x 10 4 10,200 = 1.02 x 10 8 105,000,000 = 1.05 x 10 Chemistry-1 Notes Chapter 2 Page 1 Page 1 Powers of 10 – negative exponents 0 -4 1 10 = 1 10 = 0.0001 = /10,000 -1 1 -5 1 10 = 0.1 = /10 10 = 0.00001 = /100,000 -2 1 -6 1 10 = 0.01 = /100 10 = 0.000001 = /1,000,000 -3 1 -7 10 = 0.001 10 = 0.0000001 = /1,000 1 = /10,000,000 Scientific notation of numbers less than 1 -1 0.136 = 1.36 x 10 -2 0.0560 = 5.6 x 10 -5 0.0000352 = 3.52 x 10 -6 0.00000105 = 1.05 x 10 To Review: Positive exponents tells you how many decimal places you must move the decimal point to the right to get to the real number. They indicate numbers that are greater than 1. 3 6.21 x 10 says you must move the decimal point 3 places to the right to get to the real number. 3 6.21 x 10 = 6,210. Chemistry-1 Notes Chapter 2 Page 2 Page 2 Negative exponents tells you how many decimal places you must move the decimal point to the left to get to the real number. They indicate numbers that are less than 1. 6.21 x 10–3 says you must move the decimal point 3 places to the left to get to the real number. –3 6.21 x 10 = 0.00621 Self-Check: Write the following using scientific notation. 7 a) 93,000,000 9.3 x 10 Cover -10 b) 0.000,000,000,105 1.05 x 10 Answers for Self 6 Test c) one million 1.0 x 10 -6 d) one millionth 1.0 x 10 Chemistry-1 Notes Chapter 2 Page 3 Page 3 International System of Measurements a.k.a. Metric System a.k.a. SI Metric Unit British Unit Length Meter (m) foot (ft.) Volume (space) Liter (L) quart (qt.) Mass (not weight) Gram (g) pound (lb.) Prefixes (multiples of the basic unit) Example √ kilo 1,000 x unit 1 kilogram = 1,000 grams hecto 100 x unit 1 hectogram = 100 grams deca 10 x unit 1 decagram = 10 grams --- Basic Unit --- --- 1 gram --- 1 deci 0.1 x unit ( /10) 1 decigram = 0.1 gram 1 √ centi 0.01 x unit ( /100) 1 centigram = 0.01 gram 1 √ milli 0.001 x unit ( /1,000) 1 milligram = 0.001 gram kilometer hectometer deca meter decimeter centimeter millimeter km hm dam METER dm cm mm kg hg dag GRAM dg cg mg kL hL daL LITER dL cL mL Chemistry-1 Notes Chapter 2 Page 4 Page 4 International System of Measurements a.k.a. Metric System a.k.a. SI kilometer hectometer decameter decimeter centimeter millimeter km hm dam METER dm cm mm kg hg dag GRAM dg cg mg kL hL daL LITER dL cL mL mega kilo hecto deca BasicBasic UnitUnit deci centi milli micro M k h da gram (g) (g) d c m µ 0.1 0.01 0.001 0.000001 1,000,000 1,000 100 10 literliter (L) (L) 1/ 1/ 1/ 1/ 10 100 1,000 1,000,000 6 3 2 1 –1 –2 –3 –6 10 10 10 10 metermeter (m) (m) 10 10 10 10 Chemistry-1 Notes Chapter 2 Page 5 Measuring Volume Method #1: by Linear Measurement Volume = length x width x height = L x W x H 10 cm = 10 cm x 10 cm x 10 cm = (10 x 10 x 10) (cm x cm x cm) 10 cm = 1,000 cm3 10 cm We multiplied the numbers AND the Units. 1,000 cm3 = 1 L 1 cm 1 cm 1 cm3 = 1 mL Chemistry-1 Notes Chapter 2 Page 6 Page 6 Method #2: by Water Displacement We read a graduated cylinder at the bottom of the meniscus. The units are milliliters. Remember: 1 mL = 1 cm3 to determine the volume of the object: volume of object & water volume of water = volume of object Volume of Object 79 mL 79.0 mL 38.0 mL 38 mL 41.0 mL object Chemistry-1 Notes Chapter 2 Page 7 Page 7 Measuring Liquid Volume What volume is indicated on each of the graduated cylinders below? Don’t forget to write the units. 60 30 4 50 20 3 1) 2) 3) 25 80 6 20 75 5 15 70 4 10 65 3 4) 5) 6) 40 4 30 3 50 20 2 10 1 40 7) 8) 9) Chemistry-1 Notes Chapter 2 Page 8 Page 8 Measuring Liquid Volume What volume is indicated on each of the graduated cylinders below? Don’t forget to write the units. 60 30 4 50 20 3 1) 56.0 mL 2) 4.35 mL 3) 23.5 mL 25 80 6 20 75 5 15 70 4 10 65 3 4) 16.5 mL 5) 76.0 mL 6) 5.3 mL 40 4 30 3 50 20 2 10 1 40 7) 32 mL 8) 3.5 mL 9) 47.0 mL Chemistry-1 Notes Chapter 2 Page 9 Page 9 MMeeaassuurriinngg MMaassss AAccttuuaallllyy,, mmaassss aanndd wweeiigghhtt aarree ddiiffffeerreenntt.. MMaassss iiss tthhee aammoouunntt ooff mmaatttteerr iinn aann oobbjjeecctt wwhhiillee wweeiigghhtt iiss tthhee ppuullll ooff ggrraavviittyy oonn aann oobbjjeecctt.. IIff yyoouu wweeiigghh 112200 llbbss oonn EEaarrtthh,, yyoouu’’dd wweeiigghh 2200 llbbss oonn tthhee MMoooonn,, bbuutt yyoouu’’dd ssttiillll hhaavvee tthhee ssaammee mmaassss.. WWeeiigghhtt == 112200 llbbss WWeeiigghhtt == 2200 llbbss MMaassss == 112200 llbbss MMaassss == 112200 llbbss.. MMaassss iiss mmeeaassuurreedd wwiitthh aa bbaallaannccee.. TThhiiss eelleeccttrroonniicc bbaallaannccee iiss aaccccuurraattee ttoo 00..0011 gg.. TThhee mmaassss ooff tthhee ggeeooddee iiss 3322..4477 gg 32.47 g NNoott 3322..55 gg NNoott 3322..5500 gg NNoott 3322..447700 gg Chemistry-1 Notes Chapter 2 Page 10 Page 10 TThhiiss iiss ccaalllleedd aann AAnnaallyyttiiccaall BBaallaannccee.. IItt iiss aaccccuurraattee ttoo 00..00000011 gg.. TThhee mmaassss ooff tthhee VVoolluummeettrriicc FFllaasskk && tthhee lliiqquuiidd iinnssiiddee iiss 8899..22886633 gg NNoott 8899..2299 gg NNoott 8899..33 gg NNoott 8899 gg What Is Density ? It’s the mass of each cubic centimeter of an object. It’s the mass of the object compared to its size. It’s how compact the matter is in the object. We use it to compare masses like price per pound. Chemistry-1 Notes Chapter 2 Page 11 Page 11 Measuring Density mass of the object grams Density = = 3 volume of the object mL or cm 3 The Unit of Density is always: g /cm 3 The Density of Pure Liquid Water is: 1.0 g /cm What is the density of the object whose volume was measured by water displacement to be 41.0 mL? 72.42 g You must also measure the mass of that object. Mass Floating Density = 3 D < 1.0 g /cm Volume Water 72.42 g 3 Density = D = 1.0 g /cm 41.0 mL 3 D > 1.0 g /cm Density = 1.76634146 Sinking Density = 1.77 g/cm3 HW: Questions & Problems 2.8: # 86, 92, 97, 99 Chemistry-1 Notes Chapter 2 Page 12 Page 12 Significant Figures or How Accurate Do You Have To Be? Isn’t 22 cm3 the same as 22.0 cm3? NO!! 22.0 cm3 is 10 times more accurate than 22 cm3 22 cm3 includes all measures from 21.5 cm3 to 22.4 cm3 – a spread of 0.9 cm3. 22.0 cm3 includes all measures from 21.95 cm3 to 22.04 cm3 – a spread of 0.9 cm3. When making measurements, you are as accurate as your measuring instrument. If the smallest units in a 10 mL graduate is the tenths, or 0.1 mL, Then, your measurements are to 0.1 mL; Examples: 24.0 mL; 24.7 mL not 24 mL If your electronic balance can measure to the hundredths of a gram, Then your measurements are to 0.01 g Examples: 24.00 g; 24.76 g not 24 g Chemistry-1 Notes Chapter 2 Page 13 Page 13 The significant digits of a number tells how exact that number is. 1 g is less exact than 1.0 g which is less exact than 1.00 g. Do you round off when you do computations? YES! Your answer cannot be any more accurate than your least accurate measurement 3 sig figs 4 sig figs 5 sig figs Volume = 4.03 cm x 2.413 cm x 6.3721 cm = 61.964785519 cm3 3 = 61.9 cm Answer has 3 sig figs 6.3721 cm 2.413 cm 4.03 cm Chemistry-1 Notes Chapter 2 Page 14 Page 14 Spink’s Handy Rules for Handling Numbers in Chemistry 1. Don’t round until you get to your final answer. 2. All non - zero numbers are significant.
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