Post on 28-Dec-2015
Measurements and Calculations
MeasurementsNumbers
Quantitative observations
Must consist a number and units
E.g
100 dollars
number unit
5 miles
number unit
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 10
Negative power = small valueMoving the decimal point to the right0.000035 => 3.5 x 10-5
Positive power = large valueMoving the decimal point to the left3568 = 3.568 x 103
2.1 Scientific Notation Express the following numbers in scientific
notation238,0001,500,0000.1040.00000072
2.2 UnitsPart of measurement
Require common unitsUnit system
English systemMetric system or International system (SI)
Table 2.1 Some Fundamental SI units
Physical Physical QuantityQuantity
Name of unitName of unit AbbreviationAbbreviation
MassMass kilogramkilogram kgkg
LengthLength metermeter mm
TimeTime secondsecond ss
temperaturetemperature KelvinKelvin KK
Table 2.2 The Common Used Prefixes in the Metric SystemPrefixPrefix SymbolSymbol MeaningMeaning Scientific Scientific
NotationNotation
megamega MM 1,000,0001,000,000 101066
kilokilo kk 1,0001,000 101033
decideci dd 0.10.1 1010-1-1
centicenti cc 0.010.01 1010-2-2
millimilli mm 0.0010.001 1010-3-3
micromicro µµ 0.0000010.000001 1010-6-6
nanonano nn 0.0000000010.000000001 1010-9-9
2.3 Measurements of Length, Volume and MassLength
meterVolume
cm3 or mlMass
kgWeigh
2.3 Measurements of Length, Volume and MassConsider the following objects then provide
an appropriate measurement to each object2.0 L45.0 g200 km42.0 cm3
2.4 Uncertainty in Measurement
Person Person Result of Result of MeasurementMeasurement
11 2.85 cm2.85 cm
22 2.84 cm2.84 cm
33 2.86 cm2.86 cm
44 2.85 cm2.85 cm
55 2.86 cm2.86 cm
2.4 UncertaintyEvery measurement has some degree of
uncertaintyThe first digit is the certain digitThe last digit in the measurement is the
uncertain digitDetermined by “guessing”
2.4 UncertaintyDetermine the uncertain digit (estimate digit)
in the following examples2.5460.02815000.0078
2.5 Significant FiguresRules
Nonzero integers are always significant 1, 2, 3 ……
Leading zeros are never significant 0.078 => 2 s.f
Captive zeros are always significant 103 => 3 s.f
Trailing zeros at the right end of number are significant 2.30 => 3 s.f
Exact number or counting number are never significant 2 books => none or indefinite
2.5 Significant FiguresDetermine the significant figures in each of
the following measurementsA sample of an orange contains 0.0180 g of
vitamin CA forensic chemist in a crime lab weighs a
single hair and records its mass as 0.0050060 g
The volume of soda remaining in a can after a spill is 0.09020 L
There are 30 students enrolled in the class
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?
Activity (2.1 -2.4)Determine the significant figures and the
uncertain digit in the following measurements:2.56 cm10.3 g0.006 L15 roses0.07800 lb
2.5 Round Off NumbersRules for Rounding Off
If the digit to be removed is less than 5, the preceding digit stays the same 3.13 (3 s.f) => 3.1 (2 s.f)
is equal to or greater than 5, the preceding digit is increased by 1
6.35 (3 s.f) => 6.4 6.36 (3 s.f) => 6.4
In a series of calculations, carry the extra digits through to the final result and then round off
2.5 – Determining Significant Figures in Calculation
Multiplication and DivisionReport answer with the least number of
significant figuresE.g 4.56 x 1.4 = 6.384 = 6.4
8.315 ÷ 298. = 0.027903 = 0.0279Addition and Subtraction
Report answer with the least number of decimal places
E.g 12.11 + 18.0 = 30.11 = 30.10.678 – 0.1 = 0.578 = 0.6
ExamplesWithout performing the calculations, tell how
many significant figures each answer should contain5.19 + 1.9 + 0.842 = 1081 – 7.25 =2.3 x 3.14 =
The total cost of 3 boxes of candy at $2.50 a box
ExamplesCarry out the following mathematical
operations and give each result to the correct number of significant figures5.18 x 0.0280 =116.8 – 0.33 =(3.60 x 10-3) x (8.123) ÷ 4.3 = (1.33 x 2.8) + 8.41 =
2.6 Problem Solving and Dimensional AnalysisAlso known as unit factor or factor-label
methodFirst, determined the units of the answer
Second, 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
Equality and Conversion FactorsEquality =
equivalent(English metric to English-
English)
2.54 cm = 1 in1 m = 1.094 yd 1 kg = 2.205 lb453.6 g = 1lb1L = 1.06 qt1ft3 = 28.32 L
Conversion Factor
Conversion Factors: One Step ProblemsAn 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?
Conversion Factors: Multiple – Step ProblemsThe 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?
Freezing Point / Boiling
2.7 Temperature ConversionCelsius to Kelvin
TK = ToC + 273
Kelvin to CelsiusTo
C = TK -273
Celsius to FahrenheitTo
F = 1.80 (ToC) + 32
Fahrenheit to KelvinTo
C = ToF - 32
1.80
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?
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?
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?
ExamplesIsopropyl alcohol has a density of 0.785 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.