Presentation on theme: "Measurements and Calculations"— Presentation transcript:
1 Measurements and Calculations Chapter 2Measurements and Calculations
2 Measurements Numbers Must consist a number and units E.g Quantitative observationsMust consist a number and unitsE.g
3 2.1 Scientific NotationTo show how very large or very small numbers can be expressed as the product of a number between 1 and 10 and a power of 10Negative power = small valueMoving the decimal point to the right=> 3.5 x 10-5Positive power = large valueMoving the decimal point to the left3568 = x 103
4 2.1 Scientific NotationExpress the following numbers in scientific notation238,0001,500,0000.104
5 2.2 Units Part of measurement Unit system Require common units English systemMetric system or International system (SI)
6 Table 2.1 Some Fundamental SI units Physical QuantityName of unitAbbreviationMasskilogramkgLengthmetermTimesecondstemperatureKelvinK
7 Table 2.2 The Common Used Prefixes in the Metric System SymbolMeaningScientific NotationmegaM1,000,000106kilok1,000103decid0.110-1centic0.0110-2millim0.00110-3micro10-6nanon10-9
8 2.3 Measurements of Length, Volume and Mass meterVolumecm3 or mlMasskgWeigh
9 2.3 Measurements of Length, Volume and Mass Consider the following objects then provide an appropriate measurement to each object2.0 L45.0 g200 km42.0 cm3
10 2.4 Uncertainty in Measurement PersonResult of Measurement12.85 cm22.84 cm32.86 cm45
11 2.4 Uncertainty Every measurement has some degree of uncertainty The first digit is the certain digitThe last digit in the measurement is the uncertain digitDetermined by “guessing”
12 2.4 UncertaintyDetermine the uncertain digit (estimate digit) in the following examples2.5460.02815000.0078
13 2.5 Significant Figures Rules Nonzero integers are always significant 1, 2, 3 ……Leading zeros are never significant=> 2 s.fCaptive zeros are always significant103 => 3 s.fTrailing zeros at the right end of number are significant2.30 => 3 s.fExact number or counting number are never significant2 books => none or indefinite
14 2.5 Significant FiguresDetermine the significant figures in each of the following measurementsA sample of an orange contains g of vitamin CA forensic chemist in a crime lab weighs a single hair and records its mass as gThe volume of soda remaining in a can after a spill is LThere are 30 students enrolled in the class
15 Activity (2.1 -2.4) What is the SI unit for time? What is the prefix for k? What does it mean?When do you use cm3?What is the difference between mass and weigh?
16 Activity ( )Determine the significant figures and the uncertain digit in the following measurements:2.56 cm10.3 g0.006 L15 roseslb
17 2.5 Round Off Numbers Rules for Rounding Off If the digit to be removedis less than 5, the preceding digit stays the same3.13 (3 s.f) => 3.1 (2 s.f)is equal to or greater than 5, the preceding digit is increased by 16.35 (3 s.f) => 6.46.36 (3 s.f) => 6.4In a series of calculations, carry the extra digits through to the final result and then round off
18 2.5 – Determining Significant Figures in Calculation Multiplication and DivisionReport answer with the least number of significant figuresE.g x 1.4 = = 6.48.315 ÷ 298. = =Addition and SubtractionReport answer with the least number of decimal placesE.g = = 30.10.678 – 0.1 = = 0.6
19 ExamplesWithout performing the calculations, tell how many significant figures each answer should contain=1081 – 7.25 =2.3 x 3.14 =The total cost of 3 boxes of candy at $2.50 a box
20 ExamplesCarry out the following mathematical operations and give each result to the correct number of significant figures5.18 x =116.8 – 0.33 =(3.60 x 10-3) x (8.123) ÷ 4.3 =(1.33 x 2.8) =
21 2.6 Problem Solving and Dimensional Analysis Also known as unit factor or factor-label methodFirst, determined the units of the answerSecond, multiply (or divide) conversion factor so that units are not need in the answer are cancelled out and units needed in the answer appear appropriately in either the numerator or denominator of the answer.Check for correct significant figuresAsk whether your answer makes sense
22 Equality and Conversion Factors Equality = equivalent(English metric to English-English)2.54 cm = 1 in1 m = yd1 kg = lb453.6 g = 1lb1L = 1.06 qt1ft3 = LConversion Factor
23 Conversion Factors: One Step Problems An Italian bicycle has its frame size given as 62 cm. What is the frame size in inches?A new baby weighs 7.8 lb. What is its mass in kilograms?A bottle of soda contain 2.0 L. What is its volume in quarts?
24 Conversion Factors: Multiple – Step Problems The length of the marathon race is approximate 26.2 mi. What is this distance in kilometer?How many seconds in one day?You car has a 5.00-L engine. What is the size of this engine in cubic inches?
27 2.7 Temperature Conversion Celsius to KelvinTK = ToC + 273Kelvin to CelsiusToC = TK -273Celsius to FahrenheitToF = 1.80 (ToC) + 32Fahrenheit to KelvinToC = ToF - 321.80
28 ExampleIf your body temperature is 312 K, what is it on the Celsius scale?You’re traveling in a metric county and get sick. You temperature is 39oC. What is it on the Fahrenheit scale?Pork is considered to be well done when its internal temperature reaches 160.oF. What is it on the Celsius scale?
29 2.8 DensityDefined as the amount of matter present in a given volume of substance.If each ball has the same mass, which box would weigh more? Why?
30 ExamplesA block has a volume of 25.3 cm3. Its mass is 21.7g . Calculate the density of the block.A student fills a graduated cylinder to 25.0 mL with liquid. She then immerse a solid in the liquid. The volume of the liquid rises to 33.9 ml. The mass of the solid is 63.5g. What is its density?
31 ExamplesIsopropyl alcohol has a density of g/ml. What volume should be measured to obtain 20.0 g of liquid?A beaker contains 725 mL of water. The density of water is 1.00 g/mL. Calculate the volume of water in liters. Find the mass of the water in ounces.