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.