Standard Test Procedures Manual
|
|
- Hope Simon
- 7 years ago
- Views:
Transcription
1 STP Standard Test Procedures Manual Section: GUIDELINES FOR THE USE OF SIGNIFICANT FIGURES 1. SCOPE 1.1. Description of Procedure This Procedure provides a process for the rounding of significant figures used in reporting observed or calculated values and comparing them to the specification limits. 1.2 Application of Test 2. TERMINOLOGY The following applies to all specified limits in the specification. For the purposes of determining conformance with the specification limits, an observed or calculated value shall be rounded to the nearest unit in the last right hand digit used in expressing the specification limit. The observed or calculated value shall be rounded in accordance with the method described in Section 3 of this Standard Test Procedure Significant Digit n A significant digit is any of the figures 0 through 9, except leading zeros and some trailing zeros, which is used with its place to denote a numerical quantity to some desired approximation. 2.2 Use of Zeros 0 The digit zero may either indicate a specific value or indicate place only in accordance with the following guidelines Zeros leading the first non-zero digit of a number indicate order of magnitude only and are not significant digits. For example, the number has two significant digits Zeros trailing the last non-zero digit for numbers represented with a decimal point are significant digits. For example, and both have four significant digits The significance of trailing zeros for numbers represented without the use of a decimal point can only be identified from knowledge of the source of the value. For example, a modulus strength of 140,000 Pa, may have as many as 6 and as Date: Page 1 of 6
2 few as 2 significant digits. To eliminate ambiguity, exponential notation may be used. Thus 1.40 x 10 5 Pa indicates that the modulus is reported to the nearest 0.01 x 10 5 Pa or 1,000 Pa. The use of SI prefixes is recommended to reduce the need for trailing zeros of uncertain significance. Thus, 140 kpa and Mpa each indicate that the modulus is reported to the nearest 1 kpa or 1,000 Pa while 140 kpa may have two or three significant digits. 3. PROCEDURE 3.1. Rounding Procedure The actual rounding procedure shall be as follows: When the next digit beyond the last figure to be retained is less than five, do not change the digit in the last place to be retained. For example, if a test result was found to be 5.14% and it was to be reported to the nearest 0.1%, the 4 is less than 5, so the test result would be reported as 5.1% When the next digit beyond the last figure to be retained is greater than five, increase by one the digit in the last place to be retained. For example, if a test result was found to be 5.16% and it was to be reported to the nearest 0.1%, the 6 is greater than 5, so the test result would be reported as 5.2% When the next digit beyond the last figure to be retained is five, and there are no digits beyond this five, or only zeros, increase by one the digit in the last place to be retained if it is odd, if it is even leave the digit unchanged. For example, if a test result was found to be 5.150% and it was to be reported to the nearest 0.1%, the 1 is an odd number, so the test result would be reported as 5.2%. If the test result was found to be 5.250% and it was to be reported to the nearest 0.1%, the 2 is an even number so the test result would be reported as 5.2% When the next digit beyond the last figure to be retained is five, and there are digits beyond this five, increase by one the digit in the last place to be retained. For example, if a test result was found to be 5.151% and it was to be reported to the nearest 0.1%, there are non-zero digits beyond the five so the test result would be reported as 5.2% The rounded value should be obtained in one step by direct rounding of the most precise value available and not in two or more successive roundings. For example, 89,490 Pa rounded to the nearest 1,000 Pa is 89,000 Pa. It is incorrect to first round to the nearest 100 Pa giving 89,500 Pa then to round to the nearest 1,000 Pa giving 90,000 Pa If the standard indicates that values are to be rounded to the nearest 50, 5, 0.5, 0.005, etc. the recorded or observed value should be doubled, then rounded off to the nearest 100, 10, 1, 0.1, etc. in accordance with the procedures listed in Section Date: Page: 2 of 6
3 3.1.1 to The rounded number would then be divided by two and reported. For example, in rounding 6,025 to the nearest 50, 6,025 is doubled giving 12,050. This number becomes 12,000 when rounded to the nearest 100 (using Section 3.1.3). When 12,000 is divided by 2, the resulting number, 6,000 is the rounded value of 6,025. In rounding 6,075 to the nearest 50, 6,075 is doubled giving 12,150 (using Section 3.1.3) which becomes 12,200 when rounded to the nearest 100. When 12,200 is divided by 2, the resulting number, 6,100, is the rounded value of 6, Recording Test Data Unless otherwise specified in a Standard Test Procedure, the following shall apply when recording direct measurements on a graduated cylinder, dial, or ruler. All digits known exactly from the measurement device plus one digit, which is uncertain due to estimation, should be recorded. For example, if a graduated cylinder is graduated in increments of 0.1 ml, then an observation would be recorded as 9.76 ml where it is observed between the 9.7 and 9.8 marks on the cylinder and estimated to be about six tenths of the way between those marks. When the measuring device has a vernier scale, the last digit recorded shall be the one from the vernier. 3.3 Calculations of Test Results from Test Data When calculating a test result from test data, avoid rounding of intermediate quantities. As far as is practical with the calculating device or form used, carry out calculations with the test data exactly and round only the final result. For example: Given: 1. Calculated Asphalt Content (ASPH) = % 2. Specification Limit for Asphalt Content = 5.3% ± 0.3% 3. Bulk Specific Gravity of Mix (BSGM) = Bulk Specific Gravity of Aggregate (BSG) = Specification Limit for Voids in Mineral Aggregate = 14.5 % Minimum (VMA) The asphalt content has been calculated to be exactly %. In order to compare this value against the specification limit which is significant to the nearest 0.1 % (i.e. 5.3 %), the calculated asphalt content would be rounded to the nearest 0.1 % and be reported as 5.1 % (Section 1.2 and Section 3.1.1). Date: Page: 3 of 6
4 BSGM VMA = 100x 1- = 100x 1 = % ASPH x BSG 1 + x The VMA has been exactly calculated to be %. In order to compare this value against the specification limit which is significant to the nearest 0.1% (i.e. 14.5%), the calculated VMA would be rounded to the nearest 0.1% and reported as 21.1% (Section 1.2 and Section 3.1.1). The exact asphalt content value was used in the calculation of VMA not the rounded value. This is because the calculation of Asphalt Content is an intermediate calculation in the computation of the VMA. In accordance with Section 3.3, the intermediate values should not be rounded, the final result is rounded and compared to the specification limits. 3.4 Rounding and Significant Figures (No Indication of Significant Figures) The following rules will be used to derive the number and place of significant digits to be reported if the number and place of significant digits are not defined When adding or subtracting test data the result shall contain no significant digits beyond the place of the last significant digit of any datum = 26.9, because the number 9.3 is significant to only one decimal place. The value 26.9 is obtained by rounding the exact sum of to one decimal place (Section 3.1.2) = 3, because the last significant digit of 926 is the last digit or the nearest 1. The value 3 is obtained by rounding the exact difference of 2.6 to the nearest 1 (Section 3.1.2) , ,460 = 231,000, because the number 140,000 is known to have been recorded to the nearest thousand. The value 231,000 is obtained by rounding the exact value of 231,460 to the nearest thousand (Section 3.1.1) When multiplying or dividing the result shall contain no more significant figures than the value with the least number of significant digits. Date: Page: 4 of 6
5 x 4.3 = 49, since the factor 4.3 has two significant digits the exact product, , is rounded and reported to two significant digits (Section 3.1.2). 2. ( ) = 0.6, in this case only one figure is significant because 4.3 the numerator difference has only one significant figure (Section Example 2). As a result, the exact quotient, is rounded and reported to one significant digit (Section 3.1.1) When using logarithms the digits of ln(x) or log 10 (x) are significant through the n th place after the decimal when x has n significant digits. When using exponents the number of significant digits of e x or 10 x is equal to the place of the last significant digit in x after the decimal. 1. ln(3.46) = 1.241, since 3.46 has 3 significant digits, the exact value, , is rounded and reported to 3 places after the decimal (Section 3.1.1) = 2,900, since 3.46 is significant to two places after the decimal, the exact value, 2, , is rounded and reported to two significant digits (Section 3.1.2) The rule for numbers representing exact counts or mathematical constants is that they are to be treated as having an infinite number of significant digits x = 1 = 0. 88, in this case 1 and 2 are exact constants 2 2 with two significant digits and 0.23 is a measured quantity with two significant digits. There will be two significant digits in the quotient (Section Example 2) and in the difference (Section Example 2). As a result, the exact value, 0.885, is rounded and reported to two significant digits (Section 3.1.3). 2. A count of 50 pieces times a measured thickness of mm is 50 x = 6.20 mm, since the factor of has three significant digits Date: Page: 5 of 6
6 4. REPEATABILITY 4.1 Sources of Error and the exact count of 50 has an infinite number of significant digits, the exact product, 6.2, is rounded and reported to three significant digits (Section Example 1). 3. A measurement of inches is to be converted to millimetres. The result is x 25.4 = mm, since the factor of has four significant digits and the constant value 25.4 has an infinite number of significant digits, the exact product, , is rounded and reported to four significant digits (Section and Section Example 1). Rounding test results avoids a misleading impression of precision while preventing loss of information due to coarse resolution. Any approach to retaining only the necessary significant figures involves some information loss. As a result, the level of rounding is carefully selected by considering the planned and potential uses for the data. The number of significant digits must be adequate for comparison against specification limits. For some purposes, such as where calculations involve differences of measurements that are close in magnitude and in some statistical calculations, such as Students t-tests and autocorrelations, data should be reported to at least two more significant figures than required by the specifications limits. 5. ADDED INFORMATION 5.1 References ASTM E29-93a Standard Practice for Using Significant Digits in Test Data to Determine Acceptance with Specifications. Date: Page: 6 of 6
2.2 Scientific Notation: Writing Large and Small Numbers
2.2 Scientific Notation: Writing Large and Small Numbers A number written in scientific notation has two parts. A decimal part: a number that is between 1 and 10. An exponential part: 10 raised to an exponent,
More informationFigure 1. A typical Laboratory Thermometer graduated in C.
SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES
More informationWelcome to Physics 40!
Welcome to Physics 40! Physics for Scientists and Engineers Lab 1: Introduction to Measurement SI Quantities & Units In mechanics, three basic quantities are used Length, Mass, Time Will also use derived
More informationSolving Exponential Equations
Solving Exponential Equations Deciding How to Solve Exponential Equations When asked to solve an exponential equation such as x + 6 = or x = 18, the first thing we need to do is to decide which way is
More informationA Short Guide to Significant Figures
A Short Guide to Significant Figures Quick Reference Section Here are the basic rules for significant figures - read the full text of this guide to gain a complete understanding of what these rules really
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More informationReview of Scientific Notation and Significant Figures
II-1 Scientific Notation Review of Scientific Notation and Significant Figures Frequently numbers that occur in physics and other sciences are either very large or very small. For example, the speed of
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationSection 1. Logarithms
Worksheet 2.7 Logarithms and Exponentials Section 1 Logarithms The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related
More informationCHAPTER 4 DIMENSIONAL ANALYSIS
CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.
More informationFollowing are Summaries from Two Chemistry Education Web Sites Concerning Significant Figure Rules
Following are Summaries from Two Chemistry Education Web Sites Concerning Significant Figure Rules From http://dbhs.wvusd.k12.ca.us/sigfigs/sigfigrules.html There are three rules on determining how many
More informationChapter 2 Measurement and Problem Solving
Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Graph of global Temperature rise in 20 th Century. Cover page Opposite page 11. Roy Kennedy Massachusetts Bay Community
More informationChapter 2 Measurements in Chemistry. Standard measuring device. Standard scale gram (g)
1 Chapter 2 Measurements in Chemistry Standard measuring device Standard scale gram (g) 2 Reliability of Measurements Accuracy closeness to true value Precision reproducibility Example: 98.6 o F 98.5 o
More informationEXERCISE # 1.Metric Measurement & Scientific Notation
EXERCISE # 1.Metric Measurement & Scientific Notation Student Learning Outcomes At the completion of this exercise, students will be able to learn: 1. How to use scientific notation 2. Discuss the importance
More informationFlorida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower
Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including
More informationBasic numerical skills: FRACTIONS, DECIMALS, PROPORTIONS, RATIOS AND PERCENTAGES
Basic numerical skills: FRACTIONS, DECIMALS, PROPORTIONS, RATIOS AND PERCENTAGES. Introduction (simple) This helpsheet is concerned with the ways that we express quantities that are not whole numbers,
More informationChapter 1 Lecture Notes: Science and Measurements
Educational Goals Chapter 1 Lecture Notes: Science and Measurements 1. Explain, compare, and contrast the terms scientific method, hypothesis, and experiment. 2. Compare and contrast scientific theory
More informationSimplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
MAC 1105 Final Review Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 1) 8x 2-49x + 6 x - 6 A) 1, x 6 B) 8x - 1, x 6 x -
More informationLinear Equations and Inequalities
Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................
More informationFractions to decimals
Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of
More informationIntroduction to Decimals
Introduction to Decimals Reading and Writing Decimals: Note: There is a relationship between fractions and numbers written in decimal notation. Three-tenths 10 0. 1 zero 1 decimal place Three- 0. 0 100
More informationChapter 3 Review Math 1030
Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%
More informationThe Mathematics 11 Competency Test Percent Increase or Decrease
The Mathematics 11 Competency Test Percent Increase or Decrease The language of percent is frequently used to indicate the relative degree to which some quantity changes. So, we often speak of percent
More informationMATH-0910 Review Concepts (Haugen)
Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,
More informationThis Unit: Floating Point Arithmetic. CIS 371 Computer Organization and Design. Readings. Floating Point (FP) Numbers
This Unit: Floating Point Arithmetic CIS 371 Computer Organization and Design Unit 7: Floating Point App App App System software Mem CPU I/O Formats Precision and range IEEE 754 standard Operations Addition
More informationDATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation
A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal
More information1004.6 one thousand, four AND six tenths 3.042 three AND forty-two thousandths 0.0063 sixty-three ten-thousands Two hundred AND two hundreds 200.
Section 4 Decimal Notation Place Value Chart 00 0 0 00 000 0000 00000 0. 0.0 0.00 0.000 0.0000 hundred ten one tenth hundredth thousandth Ten thousandth Hundred thousandth Identify the place value for
More informationCS321. Introduction to Numerical Methods
CS3 Introduction to Numerical Methods Lecture Number Representations and Errors Professor Jun Zhang Department of Computer Science University of Kentucky Lexington, KY 40506-0633 August 7, 05 Number in
More information3.3 Addition and Subtraction of Rational Numbers
3.3 Addition and Subtraction of Rational Numbers In this section we consider addition and subtraction of both fractions and decimals. We start with addition and subtraction of fractions with the same denominator.
More informationRecall the process used for adding decimal numbers. 1. Place the numbers to be added in vertical format, aligning the decimal points.
2 MODULE 4. DECIMALS 4a Decimal Arithmetic Adding Decimals Recall the process used for adding decimal numbers. Adding Decimals. To add decimal numbers, proceed as follows: 1. Place the numbers to be added
More informationParamedic Program Pre-Admission Mathematics Test Study Guide
Paramedic Program Pre-Admission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page
More informationSection 1.5 Exponents, Square Roots, and the Order of Operations
Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.
More informationCHAPTER 5 Round-off errors
CHAPTER 5 Round-off errors In the two previous chapters we have seen how numbers can be represented in the binary numeral system and how this is the basis for representing numbers in computers. Since any
More informationPAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE
PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9
More informationLevel 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3
Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels
More informationThe gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.
hundred million$ ten------ million$ million$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.
More informationSession 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers:
Session 9 Scientific Notation and Laws of Exponents If you have ever taken a Chemistry class, you may have encountered the following numbers: There are approximately 60,4,79,00,000,000,000,000 molecules
More informationMath 120 Final Exam Practice Problems, Form: A
Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,
More informationModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I
ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in
More informationDecimals Adding and Subtracting
1 Decimals Adding and Subtracting Decimals are a group of digits, which express numbers or measurements in units, tens, and multiples of 10. The digits for units and multiples of 10 are followed by a decimal
More informationMBA Jump Start Program
MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right
More informationCORPORATE FINANCE # 2: INTERNAL RATE OF RETURN
CORPORATE FINANCE # 2: INTERNAL RATE OF RETURN Professor Ethel Silverstein Mathematics by Dr. Sharon Petrushka Introduction How do you compare investments with different initial costs ( such as $50,000
More informationPre-Algebra Lecture 6
Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More informationUseful Number Systems
Useful Number Systems Decimal Base = 10 Digit Set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Binary Base = 2 Digit Set = {0, 1} Octal Base = 8 = 2 3 Digit Set = {0, 1, 2, 3, 4, 5, 6, 7} Hexadecimal Base = 16 = 2
More informationTo convert an arbitrary power of 2 into its English equivalent, remember the rules of exponential arithmetic:
Binary Numbers In computer science we deal almost exclusively with binary numbers. it will be very helpful to memorize some binary constants and their decimal and English equivalents. By English equivalents
More informationAddition Methods. Methods Jottings Expanded Compact Examples 8 + 7 = 15
Addition Methods Methods Jottings Expanded Compact Examples 8 + 7 = 15 48 + 36 = 84 or: Write the numbers in columns. Adding the tens first: 47 + 76 110 13 123 Adding the units first: 47 + 76 13 110 123
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material
More informationSection 4.5 Exponential and Logarithmic Equations
Section 4.5 Exponential and Logarithmic Equations Exponential Equations An exponential equation is one in which the variable occurs in the exponent. EXAMPLE: Solve the equation x = 7. Solution 1: We have
More informationHFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES
HFCC Math Lab Beginning Algebra 1 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES Before being able to solve word problems in algebra, you must be able to change words, phrases, and sentences
More informationNumber Conversions Dr. Sarita Agarwal (Acharya Narendra Dev College,University of Delhi)
Conversions Dr. Sarita Agarwal (Acharya Narendra Dev College,University of Delhi) INTRODUCTION System- A number system defines a set of values to represent quantity. We talk about the number of people
More informationYOU CAN COUNT ON NUMBER LINES
Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and
More informationNUMBER SYSTEMS. William Stallings
NUMBER SYSTEMS William Stallings The Decimal System... The Binary System...3 Converting between Binary and Decimal...3 Integers...4 Fractions...5 Hexadecimal Notation...6 This document available at WilliamStallings.com/StudentSupport.html
More informationCHAPTER 2: MEASUREMENT AND PROBLEM SOLVING
CHAPTER 2: MEASUREMENT AND PROBLEM SOLVING Problems: 1-64, 69-88, 91-120, 123-124 2.1 Measuring Global Temperatures measurement: a number with attached units When scientists collect data, it is important
More informationSection 4-7 Exponential and Logarithmic Equations. Solving an Exponential Equation. log 2. 3 2 log 5. log 2 1.4406
314 4 INVERSE FUNCTIONS; EXPONENTIAL AND LOGARITHMIC FUNCTIONS Section 4-7 Exponential and Logarithmic Equations Exponential Equations Logarithmic Equations Change of Base Equations involving exponential
More informationJobTestPrep's Numeracy Review Decimals & Percentages
JobTestPrep's Numeracy Review Decimals & Percentages 1 Table of contents What is decimal? 3 Converting fractions to decimals 4 Converting decimals to fractions 6 Percentages 6 Adding and subtracting decimals
More informationECE 0142 Computer Organization. Lecture 3 Floating Point Representations
ECE 0142 Computer Organization Lecture 3 Floating Point Representations 1 Floating-point arithmetic We often incur floating-point programming. Floating point greatly simplifies working with large (e.g.,
More informationChapter 1: Chemistry: Measurements and Methods
Chapter 1: Chemistry: Measurements and Methods 1.1 The Discovery Process o Chemistry - The study of matter o Matter - Anything that has mass and occupies space, the stuff that things are made of. This
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationLies My Calculator and Computer Told Me
Lies My Calculator and Computer Told Me 2 LIES MY CALCULATOR AND COMPUTER TOLD ME Lies My Calculator and Computer Told Me See Section.4 for a discussion of graphing calculators and computers with graphing
More informationLESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to:
LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to: 1. Change fractions to decimals. 2. Change decimals to fractions. 3. Change percents to decimals.
More information2.6 Exponents and Order of Operations
2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated
More informationCHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises
CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =
More informationAP Physics 1 and 2 Lab Investigations
AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks
More informationMath Workshop October 2010 Fractions and Repeating Decimals
Math Workshop October 2010 Fractions and Repeating Decimals This evening we will investigate the patterns that arise when converting fractions to decimals. As an example of what we will be looking at,
More information6 3 4 9 = 6 10 + 3 10 + 4 10 + 9 10
Lesson The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base- system. When you
More informationUNIT (1) MEASUREMENTS IN CHEMISTRY
UNIT (1) MEASUREMENTS IN CHEMISTRY Measurements are part of our daily lives. We measure our weights, driving distances, and gallons of gasoline. As a health professional you might measure blood pressure,
More informationOct: 50 8 = 6 (r = 2) 6 8 = 0 (r = 6) Writing the remainders in reverse order we get: (50) 10 = (62) 8
ECE Department Summer LECTURE #5: Number Systems EEL : Digital Logic and Computer Systems Based on lecture notes by Dr. Eric M. Schwartz Decimal Number System: -Our standard number system is base, also
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationMath 120 Basic finance percent problems from prior courses (amount = % X base)
Math 120 Basic finance percent problems from prior courses (amount = % X base) 1) Given a sales tax rate of 8%, a) find the tax on an item priced at $250, b) find the total amount due (which includes both
More informationCircumference and Area of a Circle
Overview Math Concepts Materials Students explore how to derive pi (π) as a ratio. Students also study the circumference and area of a circle using formulas. numbers and operations TI-30XS MultiView two-dimensional
More informationCHAPTER 2 Estimating Probabilities
CHAPTER 2 Estimating Probabilities Machine Learning Copyright c 2016. Tom M. Mitchell. All rights reserved. *DRAFT OF January 24, 2016* *PLEASE DO NOT DISTRIBUTE WITHOUT AUTHOR S PERMISSION* This is a
More informationLIES MY CALCULATOR AND COMPUTER TOLD ME
LIES MY CALCULATOR AND COMPUTER TOLD ME See Section Appendix.4 G for a discussion of graphing calculators and computers with graphing software. A wide variety of pocket-size calculating devices are currently
More informationBinary Adders: Half Adders and Full Adders
Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS - DECIMALS AND WHOLE NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More informationSummer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students
Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Studies show that most students lose about two months of math abilities over the summer when they do not engage in
More informationA.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents
Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify
More information2010/9/19. Binary number system. Binary numbers. Outline. Binary to decimal
2/9/9 Binary number system Computer (electronic) systems prefer binary numbers Binary number: represent a number in base-2 Binary numbers 2 3 + 7 + 5 Some terminology Bit: a binary digit ( or ) Hexadecimal
More informationMETRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281 Feet Metres 3.281 Feet Kilometres 0.
Linear Measure Square Measure or Area Volume or Capacity Mass Density Force* Pressure* or Stress* Temperature METRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281
More informationMeasurement of Length, Mass, Volume and Density
Measurement of Length, Mass, Volume and Density Experimental Objective The objective of this experiment is to acquaint you with basic scientific conventions for measuring physical quantities. You will
More informationMULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.
1.4 Multiplication and (1-25) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with
More informationDIVISION OF DECIMALS. 1503 9. We then we multiply by the
Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the 0 67 67 = = 9 67 67 The decimal equivalent of is. 67.
More informationWeek 13 Trigonometric Form of Complex Numbers
Week Trigonometric Form of Complex Numbers Overview In this week of the course, which is the last week if you are not going to take calculus, we will look at how Trigonometry can sometimes help in working
More informationREVIEW SHEETS BASIC MATHEMATICS MATH 010
REVIEW SHEETS BASIC MATHEMATICS MATH 010 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts that are taught in the specified math course. The sheets
More information5.1 Radical Notation and Rational Exponents
Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots
More informationSolving Compound Interest Problems
Solving Compound Interest Problems What is Compound Interest? If you walk into a bank and open up a savings account you will earn interest on the money you deposit in the bank. If the interest is calculated
More informationHow To Understand Algebraic Equations
Please use the resources below to review mathematical concepts found in chemistry. 1. Many Online videos by MiraCosta Professor Julie Harland: www.yourmathgal.com 2. Text references in red/burgundy and
More informationDecimals and other fractions
Chapter 2 Decimals and other fractions How to deal with the bits and pieces When drugs come from the manufacturer they are in doses to suit most adult patients. However, many of your patients will be very
More informationRational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have
8.6 Rational Exponents 8.6 OBJECTIVES 1. Define rational exponents 2. Simplify expressions containing rational exponents 3. Use a calculator to estimate the value of an expression containing rational exponents
More informationCURVE FITTING LEAST SQUARES APPROXIMATION
CURVE FITTING LEAST SQUARES APPROXIMATION Data analysis and curve fitting: Imagine that we are studying a physical system involving two quantities: x and y Also suppose that we expect a linear relationship
More informationRadicals - Multiply and Divide Radicals
8. Radicals - Multiply and Divide Radicals Objective: Multiply and divide radicals using the product and quotient rules of radicals. Multiplying radicals is very simple if the index on all the radicals
More informationMaths Workshop for Parents 2. Fractions and Algebra
Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)
More informationChapter 5. Decimals. Use the calculator.
Chapter 5. Decimals 5.1 An Introduction to the Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals 5.4 Dividing Decimals 5.5 Fractions and Decimals 5.6 Square Roots 5.7 Solving Equations
More informationVocabulary Cards and Word Walls Revised: June 29, 2011
Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,
More informationPURSUITS IN MATHEMATICS often produce elementary functions as solutions that need to be
Fast Approximation of the Tangent, Hyperbolic Tangent, Exponential and Logarithmic Functions 2007 Ron Doerfler http://www.myreckonings.com June 27, 2007 Abstract There are some of us who enjoy using our
More informationChapter 1: Order of Operations, Fractions & Percents
HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain
More informationProgressions for the Common Core State Standards in Mathematics (draft)
Progressions for the Common Core State Standards in Mathematics (draft) cthe Common Core Standards Writing Team 2 April 202 K 5, Number and Operations in Base Ten Overview Students work in the base-ten
More informationCOMMUNICATING using MEASUREMENTS In Engineering we use a great many measuring instruments.
COMMUNICATING using MEASUREMENTS In Engineering we use a great many measuring instruments. Scales Verniers Micrometers Gauges Comparators Thermometers Thermistors + Indicator Thermocouples + Indicator
More information.NET Standard DateTime Format Strings
.NET Standard DateTime Format Strings Specifier Name Description d Short date pattern Represents a custom DateTime format string defined by the current ShortDatePattern property. D Long date pattern Represents
More informationTHE BINARY NUMBER SYSTEM
THE BINARY NUMBER SYSTEM Dr. Robert P. Webber, Longwood University Our civilization uses the base 10 or decimal place value system. Each digit in a number represents a power of 10. For example, 365.42
More informationFirst published in 2013 by the University of Utah in association with the Utah State Office of Education.
First published in 201 by the University of Utah in association with the Utah State Office of Education. Copyright 201, Utah State Office of Education. Some rights reserved. This work is published under
More information