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Scanning QR In Objective-C
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30 Standardized Test Practice
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Math Handbook
Encoding QR In C#
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I Symbols II Measurements and Significant Digits 833 833 836
Generating QR In .NET Framework
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Printing QR-Code In VB.NET
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Isolating a Variable Square Root Property Quadratic Equations Quadratic Formula Dimensional Calculations Dimensional Analysis
Bar Code Printer In Objective-C
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Significant Digits Rounding Operations with Significant Digits
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III Fractions, Ratios, Rates, and Proportions
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Fractions Ratios Rates Proportions
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IV Exponents, Powers, Roots, and Absolute Value 839 841
Exponents Square and Cube Roots Operations with Exponents Absolute Value
The Coordinate Plane Graphing Data to Determine a Relationship Interpolating and Extrapolating Interpreting Line Graphs Linear Equations Slope Direct Variation Inverse Variation Quadratic Graphs
VIII Geometry and Trigonometry 841 843
853 856
Scientific Notation
Large Numbers Using Positive Exponents Small Numbers Using Negative Exponents Operations with Scientific Notation
Perimeter, Area, and Volume Area Under a Graph Right Triangles Trigonometric Ratios Law of Cosines and Law of Sines Inverses of Sine, Cosine, and Tangent Graphs of Trigonometric Functions
VI Equations
Order of Operations Solving Equations
843 847
IX Logarithms
Logarithms with Base b Common Logarithms Antilogarithms or Inverse Logarithms
Additional Problems Solutions for Practice Problems Tables
Color Conventions Electric Circuit Symbols SI Base Units SI Derived Units Useful Conversions Physical Constants SI Prefixes Moments of Inertia for Various Objects Densities of Some Common Substances Melting and Boiling Points of Some Substances Specific Heats of Some Common Substances
858 890 910
910 910 911 911 911 912 912 912 913 913 913
Heats of Fusion and Vaporization of Some Common Substances Coefficients of Thermal Expansion at 20 C Speed of Sound in Various Media Wavelengths of Visible Light Dielectric Constants, K (20 C) The Planets The Moon The Sun Periodic Table of the Elements The Elements Safety Symbols
913 914 914 914 914 915 915 915 916 917 918
919 927
I Symbols
change in quantity plus or minus a quantity is proportional to is equal to is approximately equal to is approximately equal to is less than or equal to is greater than or equal to is much less than is defined as a ab a(b) a a/b
a multiplied by b
a divided by b
a a logb x
square root of a absolute value of a log to the base, b, of x
II Measurements and Significant Digits
Connecting Math to Physics Math is the language of physics Using math, physicists are able to describe relationships among the measurements that they make using equations Each measurement is associated with a symbol that is used in physics equations The symbols are called variables
Significant Digits
All measured quantities are approximated and have significant digits The number of significant digits indicates the precision of the measurement Precision is a measure of exactness The number of significant digits in a measurement depends on the smallest unit on the measuring tool The digit farthest to the right in a measurement is estimated Example: What is the estimated digit for each of the measuring sticks in the figure below used to measure the length of the rod Using the lower measuring tool, the length is between 9 and 10 cm The measurement would be estimated to the nearest tenth of a centimeter If the length was exactly on the 9-cm or 10-cm mark, record it as 90 cm or 100 cm Using the upper measuring tool, the length is between 95 and 96 cm The measurement would be estimated to the nearest hundredth of a centimeter If the length was exactly on the 95-cm or 96-cm mark, record it as 950 cm or 960 cm
0 mm
0 cm
Math Handbook
All nonzero digits in a measurement are significant digits Some zeros are significant and some are not All digits between and including the first nonzero digit from the left through the last digit on the right are significant Use the following rules when determining the number of significant digits
1 2 3 4
Nonzero digits are significant Final zeros after a decimal point are significant Zeros between two significant digits are significant Zeros used only as placeholders are not significant
Example: State the number of significant digits in each measurement 50 g has two significant digits 1490 g has four significant digits 00 has one significant digit 30000 mm has five significant digits 506 s has three significant digits 304 s has three significant digits 00060 mm has two significant digits (6 and the last 0) 140 mm has two significant digits (just 1 and 4)
Using rules 1 and 2 Using rules 1 and 2 Using rules 2 and 4 Using rules 1, 2, and 3 Using rules 1 and 3 Using rules 1 and 3 Using rules 1, 2, and 4 Using rules 1 and 4
1 State the number of significant digits in each measurement a 1405 m b 250 km c 00034 m d 12007 kg e 58 106 kg f 303 10
There are two cases in which numbers are considered exact, and thus, have an infinite number of significant digits
1 Counting numbers have an infinite number of significant digits 2 Conversion factors have an infinite number of significant digits
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