PowerPoint Presentation
To show how very large or very small numbers can be expressed in
scientific notation To learn the English, metric, and SI systems of
measurement To use the metric system to measure length, volume and
mass Objectives 5.1Scientific Notation and UnitsMeasurements and
Calculations1Measurement A quantitative observation Consists of 2
parts Number Unit tells the scale being used
Measurements and Calculations2A. Scientific Notation Very large
or very small numbers can be expressed using scientific notation
The number is written as a number between 1 and 10 multiplied by 10
raised to a power. The power of 10 depends on:The number of places
the decimal point is moved. The direction the decimal point is
moved.Left Positive exponentRight Negative exponent Measurements
and Calculations3A. Scientific Notation Representing Large Numbers
Representing Small Numbers0.000167To obtain a number between 1 and
10 we must move the decimal point. 0.000167 = 1.67 10-4
Measurements and Calculations4B. Units Units provide a scale on
which to represent the results of a measurement.
Measurements and Calculations5B. Units There are 3 commonly used
unit systems.
English (used in the United States)Metric (uses prefixes to
change the size of the unit) SI (uses prefixes to change the size
of the unit)Measurements and Calculations6C. Measurements of
Length, Volume and Mass LengthFundamental unit is meter 1 meter =
39.37 inchesComparing English and metric systems
Measurements and Calculations7C. Measurements of Length, Volume
and Mass
Measurements and Calculations8C. Measurements of Length, Volume
and Mass Volume Amount of 3-D space occupied by a substance
Fundamental unit is meter3 (m3)
Measurements and Calculations9C. Measurements of Length, Volume
and Mass Mass Quantity of matter in an object Fundamental unit is
kilogram
Measurements and Calculations10C. Measurements of Length, Volume
and Mass
Measurements and Calculations11To learn how uncertainty in a
measurement arises To learn to indicate a measurements uncertainty
by using significant figures To learn to determine the number of
significant figures in a calculated result Objectives
5.2Uncertainty in Measurements and Significant FiguresMeasurements
and Calculations12A. Uncertainty in Measurement A measurement
always has some degree of uncertainty.
Measurements and Calculations13A. Uncertainty in Measurement
Different people estimate differently. Record all certain numbers
and one estimated number.
Measurements and Calculations14B. Significant Figures Numbers
recorded in a measurement. All the certain numbers plus first
estimated number Measurements and Calculations15B. Significant
Figures Rules for Counting Significant Figures Nonzero integers
always count as significant figures. 1457 4 significant figures
Measurements and Calculations16B. Significant Figures Rules for
Counting Significant Figures ZerosLeading zeros - never count0.0025
2 significant figures Captive zeros - always count 1.008 4
significant figures Trailing zeros - count only if the number is
written with a decimal point 100 1 significant figure 100. 3
significant figures 120.0 4 significant figuresMeasurements and
Calculations17B. Significant Figures Rules for Counting Significant
Figures Exact numbers - unlimited significant figures Not obtained
by measurement Determined by counting3 apples Determined by
definition1 in. = 2.54 cmMeasurements and Calculations18B.
Significant Figures
Measurements and Calculations19A digit that must be estimated is
called uncertain. A measurement always has some degree of
uncertainty.Record the certain digits and the first uncertain digit
(the estimated number).Copyright Cengage Learning. All rights
reservedMeasurements and Calculations20Measurement of Volume Using
a BuretThe volume is read at the bottom of the liquid curve
(meniscus).Meniscus of the liquid occurs at about 20.15 mL.Certain
digits: 20.15Uncertain digit: 20.15Copyright Cengage Learning. All
rights reserved
Measurements and Calculations21Significant Figures in
Measurements
Measurements and Calculations22Three differently calibrated
meter sticks are used to measure the length of a board. a) A meter
stick calibrated in a 1-m interval. b) A meter stick calibrated in
0.1-m intervals. c) A meter stick calibrated in 0.01-m intervals.
Measuring How many significant figures are reported in each
measurement?
Precision and AccuracyAccuracyCopyright Cengage Learning. All
rights reservedAgreement of a particular value with the true value.
PrecisionDegree of agreement among several measurements of the same
quantity. Measurements and Calculations23Precision and
AccuracyCopyright Cengage Learning. All rights reserved
Measurements and Calculations24
Measurements and Calculations25The distribution of darts
illustrates the difference between accuracy and precision. a) Good
accuracy and good precision: The darts are close to the bulls-eye
and to one another. b) Poor accuracy and good precision: The darts
are far from the bulls-eye but close to one another. c) Poor
accuracy and poor precision: The darts are far from the bulls-eye
and from one another.ErrorDetermining ErrorThe accepted value is
the correct value based on reliable references. The experimental
value is the value measured in the lab. The difference between the
experimental value and the accepted value is called the error.
Measurements and Calculations26ErrorThe percent error is the
absolute value of the error divided by the accepted value,
multiplied by 100%.
Measurements and Calculations27Expressing very large numbers,
such as the estimated number of stars in a galaxy, is easier if
scientific notation is used.B. Significant Figures Rules for
Multiplication and Division The number of significant figures in
the result is the same as in the measurement with the smallest
number of significant figures.
Measurements and Calculations28B. Significant Figures Rules for
Addition and Subtraction The number of significant figures in the
result is the same as in the measurement with the smallest number
of decimal places.
Measurements and Calculations29To learn how dimensional analysis
can be used to solve problems To learn the three temperature scales
To learn to convert from one temperature scale to another To
practice using problem solving techniques To define density and its
units Objectives 5.3Problem Solving and Unit
ConversionsMeasurements and Calculations30A. Tools for Problem
Solving Be systematic Ask yourself these questions Where do we want
to go? What do we know? How do we get there?Does it make sense?
Measurements and Calculations31A. Tools for Problem Solving We can
convert from one system of units to another by a method called
dimensional analysis using conversion factors. Unit1 conversion
factor = Unit2 Converting Units of Measurement Measurements and
Calculations32A. Tools for Problem Solving Conversion factors are
built from an equivalence statement which shows the relationship
between the units in different systems.Conversion factors are
ratios of the two parts of the equivalence statement that relate
the two units.Converting Units of Measurement Measurements and
Calculations33A. Tools for Problem Solving 2.85 cm = ? in.2.85 cm
conversion factor = ? in. Equivalence statement2.54 cm = 1 in.
Possible conversion factors Converting Units of MeasureDoes this
answer make sense?
Measurements and Calculations34A. Tools for Problem Solving
Tools for Converting from One Unit to Another Step 1 Find an
equivalence statement that relates the 2 units.Step 2 Choose the
conversion factor by looking at the direction of the required
change (cancel the unwanted units).Step 3 Multiply the original
quantity by the conversion factor. Step 4 Make sure you have the
correct number of significant figures. Measurements and
Calculations35B. Temperature Conversions There are three commonly
used temperature scales, Fahrenheit, Celsius and Kelvin.
Measurements and Calculations36B. Temperature Conversions Note
that The temperature unit is the same size. The zero points are
different. To convert from Celsius to Kelvin we need to adjust for
the difference in zero points. Converting Between the Kelvin and
Celsius Scales
Measurements and Calculations37B. Temperature Conversions 70. oC
= ? KTC + 273 = TK Converting Between the Kelvin and Celsius Scales
70. + 273 = 343 K
Measurements and Calculations38B. Temperature Conversions
NoteConverting Between the Fahrenheit and Celsius Scales The
different size unitsThe different zero points To convert between
Fahrenheit and Celsius we need to make 2 adjustments.
Measurements and Calculations39C. Density Density is the amount
of matter present in a given volume of substance.
Measurements and Calculations40C. Density
Measurements and Calculations41