Significant Figures IV
|
|
|
- Erick Johns
- 5 years ago
- Views:
Transcription
1 Significant Figures IV How to find the least significant figure when the answer is zero and other pesky problems related to nothing. PART IV - Those pesky zeros. copyright by James B. Condon (2013) all rights reserved Some of the graphics are supplied by Corel Corporation with their permission. Use of these materials by others is encouraged provided these notices are not altered. Donations to the Roane State Foundations would be appreciated in order to support the development of these presentations. Index: Subtraction Examples: A 0 from floating point B 0 from scientific notation. C Insignificance Ctrl Home - start Ctrl End - last slide º Next slide» Previous slide End Stop sound Home restart sound
2 Significant Figures IV Floating point subtraction Look at the following problem and determine the answer: Add the following numbers and give the answer to the proper number of significant figures. 1.52! 1.52 Of course it is zero but which zero? HUH? What say?
3 Significant Figures IV Floating point subtraction Look at the following problem and determine the answer: Add the following numbers and give the answer to the proper number of significant figures. 1.52! 1.52 Of course it is zero but which zero? OK. Let s follow the rules.
4 Significant Figures IV Floating point subtraction Look at the following problem and determine the answer: Add the following numbers and give the answer to the proper number of significant figures. 1.52! 1.52 Lining these numbers up: 1.52!1.52
5 Significant Figures IV Floating point subtraction Look at the following problem and determine the answer: Add the following numbers and give the answer to the proper number of significant figures. 1.52! and subracting: 1.52! we obtained 0.00 to the nearest 0.0x or in scientific notation: 0 10!2
6 Significant Figures IV Scientific notation For numbers that are expressed in scientific notation or have initially different number of absolution precisions, the rules do not change. Consider the following problem: What is the result of subtracting from ? Making sure one has the same factor of 10 and lining up the decimal points ! ! ! rounding =>!
7 Significant Figures IV Scientific notation For numbers that are expressed in scientific notation or have initially different number of absolution precisions, the rules do not change. Consider the following problem: What is the result of subtracting from ? Making sure one has the same factor of 10 and lining up the decimal points ! ! ! truncating =>!
8 Significant Figures IV Scientific notation For numbers that are expressed in scientific notation or have initially different number of absolution precisions, the rules do not change. Consider the following problem: What is the result of subtracting from ? The number! !4 is not in scientific notation and the negative sign is not necessary. So the final answer is: Answer = 0 10!6
9 Significant Figures IV Insignificance Another problem involves the concept of insignificance. (Again, do not confuse the word with everyday language. It does not mean the same as unimportant.) Consider the following problem. Add the following numbers: To determine rounding:
10 Significant Figures IV Insignificance Another problem involves the concept of insignificance. (Again, do not confuse the word with everyday language. It does not mean the same as unimportant.) Consider the following problem. Add the following numbers: Truncating
11 Significant Figures IV Insignificance Another problem involves the concept of insignificance. (Again, do not confuse the word with everyday language. It does not mean the same as unimportant.) Thus: Notice, then, that adding the number 4.5 to yields , i.e. the same number.
12 Significant Figures IV Insignificance Another problem involves the concept of insignificance. (Again, do not confuse the word with everyday language. It does not mean the same as unimportant.) Thus: << The number 4.5 is then said to be insignificant with respect to
Approximations and Errors
The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 3 Approximations and Errors Associate Prof. Mazen Abualtayef Civil Engineering Department,
Calculations with Sig Figs
Calculations with Sig Figs When you make calculations using data with a specific level of uncertainty, it is important that you also report your answer with the appropriate level of uncertainty (i.e.,
Chapter 4 Section 2 Operations on Decimals
Chapter 4 Section 2 Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers.
Floating Point. The World is Not Just Integers. Programming languages support numbers with fraction
1 Floating Point The World is Not Just Integers Programming languages support numbers with fraction Called floating-point numbers Examples: 3.14159265 (π) 2.71828 (e) 0.000000001 or 1.0 10 9 (seconds in
1.3.B Significant Figures
1.3.B Significant Figures The Scientific Method starts with making observations = precise and accurate measurements 1.3.3. Significant Figures (Significant Digits) 1.3.4. Round Off Error Measurement and
Exponential Numbers ID1050 Quantitative & Qualitative Reasoning
Exponential Numbers ID1050 Quantitative & Qualitative Reasoning In what ways can you have $2000? Just like fractions, you can have a number in some denomination Number Denomination Mantissa Power of 10
Rev Name Date. . Round-off error is the answer to the question How wrong is the rounded answer?
Name Date TI-84+ GC 7 Avoiding Round-off Error in Multiple Calculations Objectives: Recall the meaning of exact and approximate Observe round-off error and learn to avoid it Perform calculations using
1.3 Floating Point Form
Section 1.3 Floating Point Form 29 1.3 Floating Point Form Floating point numbers are used by computers to approximate real numbers. On the surface, the question is a simple one. There are an infinite
MA 1128: Lecture 02 1/22/2018
MA 1128: Lecture 02 1/22/2018 Exponents Scientific Notation 1 Exponents Exponents are used to indicate how many copies of a number are to be multiplied together. For example, I like to deal with the signs
Lecture 2: Python Arithmetic
Lecture 2: Python Arithmetic CS1068+ Introductory Programming in Python Dr Kieran T. Herley 2018/19 Department of Computer Science University College Cork Basic data types in Python Python data types Programs
Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Lecture 3
Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Instructor: Nicole Hynes nicole.hynes@rutgers.edu 1 Fixed Point Numbers Fixed point number: integer part
Chapter 03: Computer Arithmetic. Lesson 09: Arithmetic using floating point numbers
Chapter 03: Computer Arithmetic Lesson 09: Arithmetic using floating point numbers Objective To understand arithmetic operations in case of floating point numbers 2 Multiplication of Floating Point Numbers
Module 2: Computer Arithmetic
Module 2: Computer Arithmetic 1 B O O K : C O M P U T E R O R G A N I Z A T I O N A N D D E S I G N, 3 E D, D A V I D L. P A T T E R S O N A N D J O H N L. H A N N E S S Y, M O R G A N K A U F M A N N
Divide: Paper & Pencil
Divide: Paper & Pencil 1001 Quotient Divisor 1000 1001010 Dividend -1000 10 101 1010 1000 10 Remainder See how big a number can be subtracted, creating quotient bit on each step Binary => 1 * divisor or
15213 Recitation 2: Floating Point
15213 Recitation 2: Floating Point 1 Introduction This handout will introduce and test your knowledge of the floating point representation of real numbers, as defined by the IEEE standard. This information
fractional quantities are typically represented in computers using floating point format this approach is very much similar to scientific notation
Floating Point Arithmetic fractional quantities are typically represented in computers using floating point format this approach is very much similar to scientific notation for example, fixed point number
Significant Figures & Scientific Notation
Significant Figures & Scientific Notation Measurements are important in science (particularly chemistry!) Quantity that contains both a number and a unit Must be able to say how correct a measurement is
Scientific Notation. A measurement written in scientific notation consists of: 1. a between 1 and 9.99 followed by 2. a of 10.
Scientific Notation A measurement written in scientific notation consists of: 1. a between 1 and 9.99 followed by 2. a of 10. The number in front of the power of 10 is called the. When creating coefficients,
FLOATING POINT NUMBERS
Exponential Notation FLOATING POINT NUMBERS Englander Ch. 5 The following are equivalent representations of 1,234 123,400.0 x 10-2 12,340.0 x 10-1 1,234.0 x 10 0 123.4 x 10 1 12.34 x 10 2 1.234 x 10 3
Significant Figures. For example. Let s try this one. Introduction to Significant Figures & Scientific Notation
Significant Figures Introduction to Significant Figures & Scientific Notation Scientist use to determine how a measurement is. Significant digits in a measurement include all of the plus one. For example
Section 1.5. Finding Linear Equations
Section 1.5 Finding Linear Equations Using Slope and a Point to Find an Equation of a Line Example Find an equation of a line that has slope m = 3 and contains the point (2, 5). Solution Substitute m =
Floating Point Numbers
Floating Point Numbers Summer 8 Fractional numbers Fractional numbers fixed point Floating point numbers the IEEE 7 floating point standard Floating point operations Rounding modes CMPE Summer 8 Slides
Floating Point Representation in Computers
Floating Point Representation in Computers Floating Point Numbers - What are they? Floating Point Representation Floating Point Operations Where Things can go wrong What are Floating Point Numbers? Any
Real Numbers. range -- need to deal with larger range, not just [not just -2^(n-1) to +2^(n-1)-1] - large numbers - small numbers (fractions)
![Real Numbers. range -- need to deal with larger range, not just [not just -2^(n-1) to +2^(n-1)-1] - large numbers - small numbers (fractions)](/thumbs/89/98545356.jpg "Real Numbers. range -- need to deal with larger range, not just [not just -2^(n-1) to +2^(n-1)-1] - large numbers - small numbers (fractions)")
Real Numbers range -- need to deal with larger range, not just [not just -2^(n-1) to +2^(n-1)-1] - large numbers - small numbers (fractions) Real Numbers von Neumann recommended using fixed point with
Floating Point Arithmetic
Floating Point Arithmetic Clark N. Taylor Department of Electrical and Computer Engineering Brigham Young University clark.taylor@byu.edu 1 Introduction Numerical operations are something at which digital
Measurements: Significant Figures
Measurements: Significant Figures Significant figures: all digits in a number representing data or results that are known with certainty plus one uncertain digit. Ruler A: The last digit in a number associated
What Every Programmer Should Know About Floating-Point Arithmetic
What Every Programmer Should Know About Floating-Point Arithmetic Last updated: October 15, 2015 Contents 1 Why don t my numbers add up? 3 2 Basic Answers 3 2.1 Why don t my numbers, like 0.1 + 0.2 add
Content Design Structure, Scope & Sequence of Mathematics Content Addressed Within Numbers Up! Volcanic Panic
4-6 1-2 Number Range 1-5 Compares equivalent and non-equivalent sets by matching there are more bees than hives Uses ordinal language first to fifth 3-4 Number Range 1-10 Compares equivalent and non-equivalent
Representation of Non Negative Integers
Representation of Non Negative Integers In each of one s complement and two s complement arithmetic, no special steps are required to represent a non negative integer. All conversions to the complement
Introduction to Computer Systems Recitation 2 May 29, Marjorie Carlson Aditya Gupta Shailin Desai
Introduction to Computer Systems Recitation 2 May 29, 2014 Marjorie Carlson Aditya Gupta Shailin Desai 1 Agenda! Goal: translate any real number (plus some!) into and out of machine representation.! Integers!
Home brewed code for conversion of single precision float value to string
Home brewed code for conversion of single precision float value to string When doing microcontroller programming one may have come across a task of converting a float value to a string. For example when
On a 64-bit CPU. Size/Range vary by CPU model and Word size.
On a 64-bit CPU. Size/Range vary by CPU model and Word size. unsigned short x; //range 0 to 65553 signed short x; //range ± 32767 short x; //assumed signed There are (usually) no unsigned floats or doubles.
PRE-ALGEBRA PREP. Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., 2002.
PRE-ALGEBRA PREP Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., 2002. Course Description: The students entering prep year have
Chapter 3: Arithmetic for Computers
Chapter 3: Arithmetic for Computers Objectives Signed and Unsigned Numbers Addition and Subtraction Multiplication and Division Floating Point Computer Architecture CS 35101-002 2 The Binary Numbering
Floating-Point Arithmetic
Floating-Point Arithmetic 1 Numerical Analysis a definition sources of error 2 Floating-Point Numbers floating-point representation of a real number machine precision 3 Floating-Point Arithmetic adding
YEAR 5. Carbeile Junior School Mathematics Planning Framework. Sequence 1. Sequence 2. Sequence 3. Sequence 4
YEAR 5 1 count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 solve number problems and practical problems that involve all of the above round decimals with two to
Revision on fractions and decimals
Revision on fractions and decimals Fractions 1. Addition and subtraction of fractions (i) For same denominator, only need to add the numerators, then simplify the fraction Example 1: " + $ " = &$ " (they
In this lesson you will learn: how to add and multiply positive binary integers how to work with signed binary numbers using two s complement how fixed and floating point numbers are used to represent
Chapter 1 & 2 Calculator Test Study Guide
Chapter 1 & 2 Calculator Test Study Guide Powers and Exponents 1) To put a number to the second power, simply hit the x 2 key, then enter. 2) To put a number to the third or a higher power, key in base,
COSC 243. Data Representation 3. Lecture 3 - Data Representation 3 1. COSC 243 (Computer Architecture)
COSC 243 Data Representation 3 Lecture 3 - Data Representation 3 1 Data Representation Test Material Lectures 1, 2, and 3 Tutorials 1b, 2a, and 2b During Tutorial a Next Week 12 th and 13 th March If you
CO212 Lecture 10: Arithmetic & Logical Unit
CO212 Lecture 10: Arithmetic & Logical Unit Shobhanjana Kalita, Dept. of CSE, Tezpur University Slides courtesy: Computer Architecture and Organization, 9 th Ed, W. Stallings Integer Representation For
Mark Important Points in Margin. Significant Figures. Determine which digits in a number are significant.
Knowledge/Understanding: How and why measurements are rounded. Date: How rounding and significant figures relate to precision and uncertainty. When significant figures do not apply. Skills: Determine which
Set up and use a proportion
Daily Do Question from last class Set up and use a proportion If you are driving 70 miles per hour and you have 280 miles to go on the highway part of your trip. How long will it take? adding, subtracting,
Numeric Variable Storage Pattern
Numeric Variable Storage Pattern Sreekanth Middela Srinivas Vanam Rahul Baddula Percept Pharma Services, Bridgewater, NJ ABSTRACT This paper presents the Storage pattern of Numeric Variables within the
Number Systems and Binary Arithmetic. Quantitative Analysis II Professor Bob Orr
Number Systems and Binary Arithmetic Quantitative Analysis II Professor Bob Orr Introduction to Numbering Systems We are all familiar with the decimal number system (Base 10). Some other number systems
Lecture Objectives. Structured Programming & an Introduction to Error. Review the basic good habits of programming
Structured Programming & an Introduction to Error Lecture Objectives Review the basic good habits of programming To understand basic concepts of error and error estimation as it applies to Numerical Methods
Floating-point representations
Lecture 10 Floating-point representations Methods of representing real numbers (1) 1. Fixed-point number system limited range and/or limited precision results must be scaled 100101010 1111010 100101010.1111010
6.25 x Type the given number into the calculator. 2. Click Mode, and select SCI. Then hit enter twice
Name Date: Lesson 1-4: Scientific Notation Learning Goals: #1: How do we convert in and out of scientific notation? Scientific Notation Scientific Notation is a way of writing numbers that accommodates
Floating-point representations
Lecture 10 Floating-point representations Methods of representing real numbers (1) 1. Fixed-point number system limited range and/or limited precision results must be scaled 100101010 1111010 100101010.1111010
Signed Multiplication Multiply the positives Negate result if signs of operand are different
Another Improvement Save on space: Put multiplier in product saves on speed: only single shift needed Figure: Improved hardware for multiplication Signed Multiplication Multiply the positives Negate result
Notes for Unit 1 Part A: Rational vs. Irrational
Notes for Unit 1 Part A: Rational vs. Irrational Natural Number: Whole Number: Integer: Rational Number: Irrational Number: Rational Numbers All are Real Numbers Integers Whole Numbers Irrational Numbers
Number Systems CHAPTER Positional Number Systems
CHAPTER 2 Number Systems Inside computers, information is encoded as patterns of bits because it is easy to construct electronic circuits that exhibit the two alternative states, 0 and 1. The meaning of
Floating Point Arithmetic
Floating Point Arithmetic Computer Systems, Section 2.4 Abstraction Anything that is not an integer can be thought of as . e.g. 391.1356 Or can be thought of as + /
1. Introduction to Microsoft Excel
1. Introduction to Microsoft Excel A spreadsheet is an online version of an accountant's worksheet, which can automatically do most of the calculating for you. You can do budgets, analyze data, or generate
Foundations of Computer Systems
18-600 Foundations of Computer Systems Lecture 4: Floating Point Required Reading Assignment: Chapter 2 of CS:APP (3 rd edition) by Randy Bryant & Dave O Hallaron Assignments for This Week: Lab 1 18-600
(Refer Slide Time: 02:59)
Numerical Methods and Programming P. B. Sunil Kumar Department of Physics Indian Institute of Technology, Madras Lecture - 7 Error propagation and stability Last class we discussed about the representation
Julia Calculator ( Introduction)
Julia Calculator ( Introduction) Julia can replicate the basics of a calculator with the standard notations. Binary operators Symbol Example Addition + 2+2 = 4 Substraction 2*3 = 6 Multify * 3*3 = 9 Division
Benchmarks Addressed. Quizzes. Strand IV, S 1-2, 1-4, 2-1, 2-2, 2-3, 3-1. Journal writing. Projects. Worksheets
August/September The Decimal System Translating English words into Decimal Notation What is the decimal system? Str IV, S 1-2, 1-4, 2-1, 2-2, 2-3, 3-1 Estimating Decimals What is a number line? Changing
3.1 DATA REPRESENTATION (PART C)
3.1 DATA REPRESENTATION (PART C) 3.1.3 REAL NUMBERS AND NORMALISED FLOATING-POINT REPRESENTATION In decimal notation, the number 23.456 can be written as 0.23456 x 10 2. This means that in decimal notation,
The Perils of Floating Point
The Perils of Floating Point by Bruce M. Bush Copyright (c) 1996 Lahey Computer Systems, Inc. Permission to copy is granted with acknowledgement of the source. Many great engineering and scientific advances
Giving credit where credit is due
JDEP 284H Foundations of Computer Systems Floating Point Dr. Steve Goddard goddard@cse.unl.edu Giving credit where credit is due Most of slides for this lecture are based on slides created by Drs. Bryant
Summer Assignment Glossary
Algebra 1.1 Summer Assignment Name: Date: Hour: Directions: Show all work for full credit using a pencil. Circle your final answer. This assignment is due the first day of school. Use the summer assignment
Floating Point Representation. CS Summer 2008 Jonathan Kaldor
Floating Point Representation CS3220 - Summer 2008 Jonathan Kaldor Floating Point Numbers Infinite supply of real numbers Requires infinite space to represent certain numbers We need to be able to represent
SOLUTION: Because the fractions have a common denominator, compare the numerators. 5 < 3
Section 1 Practice Problems 1. Because the fractions have a common denominator, compare the numerators. 5 < 3 So,. 2. 0.71 To compare these numbers, write both fractions as a decimal. 0.8 is greater than
Chapter 3. Errors and numerical stability
Chapter 3 Errors and numerical stability 1 Representation of numbers Binary system : micro-transistor in state off 0 on 1 Smallest amount of stored data bit Object in memory chain of 1 and 0 10011000110101001111010010100010
Finite arithmetic and error analysis
Finite arithmetic and error analysis Escuela de Ingeniería Informática de Oviedo (Dpto de Matemáticas-UniOvi) Numerical Computation Finite arithmetic and error analysis 1 / 45 Outline 1 Number representation:
1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM
1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1.1 Introduction Given that digital logic and memory devices are based on two electrical states (on and off), it is natural to use a number
A complement number system is used to represent positive and negative integers. A complement number system is based on a fixed length representation
Complement Number Systems A complement number system is used to represent positive and negative integers A complement number system is based on a fixed length representation of numbers Pretend that integers
Operators. Java Primer Operators-1 Scott MacKenzie = 2. (b) (a)
Operators Representing and storing primitive data types is, of course, essential for any computer language. But, so, too, is the ability to perform operations on data. Java supports a comprehensive set
Computer Architecture and System Software Lecture 02: Overview of Computer Systems & Start of Chapter 2
Computer Architecture and System Software Lecture 02: Overview of Computer Systems & Start of Chapter 2 Instructor: Rob Bergen Applied Computer Science University of Winnipeg Announcements Website is up
Floating-point Arithmetic. where you sum up the integer to the left of the decimal point and the fraction to the right.
Floating-point Arithmetic Reading: pp. 312-328 Floating-Point Representation Non-scientific floating point numbers: A non-integer can be represented as: 2 4 2 3 2 2 2 1 2 0.2-1 2-2 2-3 2-4 where you sum
9. Elementary Algebraic and Transcendental Scalar Functions
Scalar Functions Summary. Introduction 2. Constants 2a. Numeric Constants 2b. Character Constants 2c. Symbol Constants 2d. Nested Constants 3. Scalar Functions 4. Arithmetic Scalar Functions 5. Operators
10.1. Unit 10. Signed Representation Systems Binary Arithmetic
0. Unit 0 Signed Representation Systems Binary Arithmetic 0.2 BINARY REPRESENTATION SYSTEMS REVIEW 0.3 Interpreting Binary Strings Given a string of s and 0 s, you need to know the representation system
Chapter Three. Arithmetic
Chapter Three 1 Arithmetic Where we've been: Performance (seconds, cycles, instructions) Abstractions: Instruction Set Architecture Assembly Language and Machine Language What's up ahead: Implementing
Floating Point January 24, 2008
15-213 The course that gives CMU its Zip! Floating Point January 24, 2008 Topics IEEE Floating Point Standard Rounding Floating Point Operations Mathematical properties class04.ppt 15-213, S 08 Floating
CS/COE0447: Computer Organization
CS/COE0447: Computer Organization and Assembly Language Chapter 3 Sangyeun Cho Dept. of Computer Science Five classic components I am like a control tower I am like a pack of file folders I am like a conveyor
CS/COE0447: Computer Organization
Five classic components CS/COE0447: Computer Organization and Assembly Language I am like a control tower I am like a pack of file folders Chapter 3 I am like a conveyor belt + service stations I exchange
Data Representation in Computer Memory
Data Representation in Computer Memory Data Representation in Computer Memory Digital computer stores the data in the form of binary bit sequences. Binary number system has two symbols: 0 and 1, called
4.1 QUANTIZATION NOISE
DIGITAL SIGNAL PROCESSING UNIT IV FINITE WORD LENGTH EFFECTS Contents : 4.1 Quantization Noise 4.2 Fixed Point and Floating Point Number Representation 4.3 Truncation and Rounding 4.4 Quantization Noise
Introduction to Computer Science-103. Midterm
Introduction to Computer Science-103 Midterm 1. Convert the following hexadecimal and octal numbers to decimal without using a calculator, showing your work. (6%) a. (ABC.D) 16 2748.8125 b. (411) 8 265
Primitive Types. Four integer types: Two floating-point types: One character type: One boolean type: byte short int (most common) long
Primitive Types Four integer types: byte short int (most common) long Two floating-point types: float double (most common) One character type: char One boolean type: boolean 1 2 Primitive Types, cont.
Table : IEEE Single Format ± a a 2 a 3 :::a 8 b b 2 b 3 :::b 23 If exponent bitstring a :::a 8 is Then numerical value represented is ( ) 2 = (
Floating Point Numbers in Java by Michael L. Overton Virtually all modern computers follow the IEEE 2 floating point standard in their representation of floating point numbers. The Java programming language
Introduction to Computers and Programming. Numeric Values
Introduction to Computers and Programming Prof. I. K. Lundqvist Lecture 5 Reading: B pp. 47-71 Sept 1 003 Numeric Values Storing the value of 5 10 using ASCII: 00110010 00110101 Binary notation: 00000000
IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1
IT 1204 Section 2.0 Data Representation and Arithmetic 2009, University of Colombo School of Computing 1 What is Analog and Digital The interpretation of an analog signal would correspond to a signal whose
CHAPTER 5: Representing Numerical Data
CHAPTER 5: Representing Numerical Data The Architecture of Computer Hardware and Systems Software & Networking: An Information Technology Approach 4th Edition, Irv Englander John Wiley and Sons 2010 PowerPoint
Lesson 3: Solving Equations; Floating-point Computation
Lesson 3: Solving Equations; Floating-point Computation restart; A hard equation Last time we were looking at this equation. eq := * sin() = Pi/2; (1.1) Maple didn't know the solutions. solve(eq,,allsolutions);
Python Programming Exercises 1
Python Programming Exercises 1 Notes: throughout these exercises >>> preceeds code that should be typed directly into the Python interpreter. To get the most out of these exercises, don t just follow them
1) Complete problems 1-65 on pages You are encouraged to use the space provided.
Dear Accelerated Pre-Calculus Student (017-018), I am excited to have you enrolled in our class for next year! We will learn a lot of material and do so in a fairly short amount of time. This class will
IEEE Standard for Floating-Point Arithmetic: 754
IEEE Standard for Floating-Point Arithmetic: 754 G.E. Antoniou G.E. Antoniou () IEEE Standard for Floating-Point Arithmetic: 754 1 / 34 Floating Point Standard: IEEE 754 1985/2008 Established in 1985 (2008)
Floating Point. EE 109 Unit 20. Floating Point Representation. Fixed Point
2.1 Floating Point 2.2 EE 19 Unit 2 IEEE 754 Floating Point Representation Floating Point Arithmetic Used to represent very numbers (fractions) and very numbers Avogadro s Number: +6.247 * 1 23 Planck
Scientific Notation & Significant Figures. Mergenthaler Vo-Tech HS Mrs. Judith B. Abergos Chemistry 2013
Scientific Notation & Significant Figures Mergenthaler Vo-Tech HS Mrs. Judith B. Abergos Chemistry 2013 Significant Figures Significant Figures digits that show how precise a measurement is The more significant
NZ Mathematics Level 1-Yr 9 Curriculum Objectives Addressed Within Numbers Up! Volcanic Panic
4-7 1-11 1 Number Count, order and compare numbers up to 5, then later to 9, and then up to 20. Make sets up to 5 (then 9, then 20). Explore the number system from zero to 99 Rote count from zero to 99
2.) = 7.) Find the unit rate of 6 miles in 20 minutes. 4.) 6 8 = 8.) Put in simplified exponential form (8 3 )(8 6 )
Warm Up Do you remember how to... 1.) 3 + 9 = Wobble Chairs: Braden, Weston, & Avalon 6.) Put 3,400,000 in scientific notation? 2.) 2 + 8 = 7.) Find the unit rate of 6 miles in 20 minutes. 3.) 2 17 = 4.)
EE 109 Unit 19. IEEE 754 Floating Point Representation Floating Point Arithmetic
1 EE 109 Unit 19 IEEE 754 Floating Point Representation Floating Point Arithmetic 2 Floating Point Used to represent very small numbers (fractions) and very large numbers Avogadro s Number: +6.0247 * 10
unused unused unused unused unused unused
BCD numbers. In some applications, such as in the financial industry, the errors that can creep in due to converting numbers back and forth between decimal and binary is unacceptable. For these applications
AMTH142 Lecture 10. Scilab Graphs Floating Point Arithmetic
AMTH142 Lecture 1 Scilab Graphs Floating Point Arithmetic April 2, 27 Contents 1.1 Graphs in Scilab......................... 2 1.1.1 Simple Graphs...................... 2 1.1.2 Line Styles........................
CS429: Computer Organization and Architecture
CS429: Computer Organization and Architecture Dr. Bill Young Department of Computer Sciences University of Texas at Austin Last updated: September 18, 2017 at 12:48 CS429 Slideset 4: 1 Topics of this Slideset
Section 1.4 Mathematics on the Computer: Floating Point Arithmetic
Section 1.4 Mathematics on the Computer: Floating Point Arithmetic Key terms Floating point arithmetic IEE Standard Mantissa Exponent Roundoff error Pitfalls of floating point arithmetic Structuring computations
CS321. Introduction to Numerical Methods
CS31 Introduction to Numerical Methods Lecture 1 Number Representations and Errors Professor Jun Zhang Department of Computer Science University of Kentucky Lexington, KY 40506 0633 August 5, 017 Number
Roundoff Errors and Computer Arithmetic
Jim Lambers Math 105A Summer Session I 2003-04 Lecture 2 Notes These notes correspond to Section 1.2 in the text. Roundoff Errors and Computer Arithmetic In computing the solution to any mathematical problem,