...NUMBER SYSTEMS TUTORIAL Courtesy of: thevbprogrammer.com Number Systems Number Systems Concepts The study of number systems is useful to the student of computing due to the fact that number systems other than the familiar decimal (base 10) number system are used in the computer field. Digital computers internally use the binary (base 2) number system to represent data and perform arithmetic calculations. The binary number system is very efficient for computers, but not for humans. Representing even relatively small numbers with the binary system requires working with long strings of ones and zeroes. The hexadecimal (base 16) number system (often called "hex" for short) provides us with a shorthand method of working with binary numbers. One digit in hex corresponds to four binary digits (bits), so the internal representation of one byte can be represented either by eight binary digits or two hexadecimal digits. Less commonly used is the octal (base 8) number system, where one digit in octal corresponds to three binary digits (bits). In the event that a computer user (programmer, operator, end user, etc.) needs to examine a display of the internal representation of computer data (such a display is called a "dump"), viewing the data in a "shorthand" representation (such as hex or octal) is less tedious than viewing the data in binary representation. The binary, hexadecimal , and octal number systems will be looked at in the following pages. The decimal number system that...
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...Introduction This Child Study Assessment will focus on the concept of place value and the base ten number system, principally focusing on the pedagogy of these concepts. It will also discuss diagnostic assessment and the misunderstandings a student acquires, which require pedagogies to alleviate and develop conceptual understanding. Part A - Diagnostic Assessment Diagnostic assessment is essential for gaining an initial understanding of what students know about a concept or topic. An effective diagnostic assessment is a one on one interview, as these predominately uncover information not obtained by written assessments and are a necessary tool which helps to direct a student’s learning (Burns, 2007). These interviews allow for an understanding...
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...all the whole numbers between 1 and n, where n must always be positive. For example 0! is a special case factorial. This is special because there are no positive numbers less than zero and we defined a factorial as a product of the numbers between n and 1. We say that 0! = 1 by claiming that the product of no numbers is 1. The reasoning and mathematics behind this is complicated and beyond the scope of this page, so let's just accept 0! as equal to 1. This works out to be mathematically true and allows us to redefine n! as follows: For example The above allows us to manipulate factorials and break them up, which is useful in combinations and permutations. Useful Factorial Properties The last two properties are important to remember. The factorial sign DOES NOT distribute across addition and subtraction. Permutations and Combinations Permutations and Combinations in mathematics both refer to different ways of arranging a given set of variables. Permutations are not strict when it comes to the order of things while Combinations are. For example; given the letters abc The Permutations are listed as follows Combinations on the other hand are considered different, all the above are considered the same since they have the exact same letters only arranged different. In other words, in combination, you can't just rearrange the same letters and then claim to have a completely different combination. Combinations are done differently: Given abc, we can make a number of combinations...
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...Study Guide Modern Plumbing, Part 1 Contents Contents INSTRUCTION TO STUDENTS LESSON ASSIGNMENTS LESSON 1: FUNDAMENTALS OF PLUMBING, PART 1 LESSON 1—EXAMINATION LESSON 2: FUNDAMENTALS OF PLUMBING, PART 2 LESSON 2—EXAMINATION LESSON 3: WATER SUPPLY AND FIXTURES LESSON 3—EXAMINATION LESSON 4: FITTINGS, VALVES, AND HEATERS LESSON 4—EXAMINATION TEST YOUR KNOWLEDGE ANSWERS 1 5 7 49 55 67 73 81 85 95 99 iii INTRODUCTION This part of your program is based on the textbook, Modern Plumbing. It’s divided into 16 assignments; each assignment covers a specific area of the plumbing trade. The study material for this part of your program consists of 1. Your textbook, Modern Plumbing. It contains the assigned readings and review exercises at the end of each unit. These are assigned as self-check exercises. 2. This study guide, which contains the following features: I Instructions Instructions An assignment page that lists all of the reading assignments for your textbook Introductions to your lessons Listings of the self-check tests you should complete as part of each assignment Answers to the self-check exercises The examinations for each lesson I I I I As you now know, your textbook is covered by the reading assignments in this guide. Your textbook, Modern Plumbing, is the heart of this program. It’s very important that you read the material in the text and study it until you’re completely familiar with it. This is the material on which your examinations...
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...Microsoft Access users can make tables with the customer’s advice, forms, reports on the animals, their care, and the customer’s payment history. Microsoft Access puts all the information combined composing a relationship between all the data entered. The tables made within the Microsoft Access database can include the information on the animals, and all the records of care given to each person’s animal. Microsoft has the capability to make these reports to provide an analysis of the data. The Microsoft Access database contains a query interface that lets the data to be inserted, and reports for printing. With Microsoft Access the person can change the old record filing system to the database system with gratification, and create records for the animals, the care provided, the animals owner name, address, phone numbers, and payments received or overdue balances. Situation 2: Frank has created a database to inventory his customers’ past due accounts to ensure that he receives payment. He has created two tables: one for...
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...INDIA The history of maths in india is very great & eventful.Indians gave the system of numerals, zero, geometry & equations to the world. The great Indian mathematician Aryabhata (476-529) wrote the Aryabhatiya ─ a volume of 121 verses. Apart from discussing astronomy, he laid down procedures of arithmetic, geometry, algebra and trigonometry. He calculated the value of Pi at 3.1416 and covered subjects like numerical squares and cube roots. Aryabhata is credited with the emergence of trigonometry through sine functions. Around the beginning of the fifteenth century Madhava (1350-1425) developed his own system of calculus based on his knowledge of trigonometry. He was an untutored mathematician from Kerala, and preceded Newton and Liebnitz by a century. The twentieth-century genius Srinivas Ramanujan (1887-1920) developed a formula for partitioning any natural number, expressing an integer as the sum of squares, cubes, or higher power of a few integers. Origin of Zero and the Decimal System The zero was known to the ancient Indians and most probably the knowledge of it spread from India to other cultures. Brahmagupta (598-668),who had worked on mathematics and astronomy, was the head of the astronomy observatory in Ujjain, which was at that point of time, the foremost mathematical centre in India; he and Bhaskar the second (1114-1185), who reached understanding on the number systems and solving equations, have together provided many rules for arithmetical operations...
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...Assignment 2: Number Sense Part One: Primary Source: Starr, Libertus, & Brannon (2013) Review the research article to answer the following questions: 1. The purpose of this research was to demonstrate a relationship between ANS acuity during infancy and math achievement later in childhood. 2. This research was conducted using a longitudinal study design of 6 month old infants and 3 and a half year old children. 3. Researchers define the approximate number system as a cognitive ability that allows us to infer an approximation of numbers without the need to count or rely on numerical symbols. 4. It was important for researchers to test ANS before formal education because learning the early math concepts such as the verbal counting system may make ANS acuity greater. 6 month old infants are not familiar with verbal or written...
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...you go out for dinner, when you’re at work, and even when you’re asleep. We are always using some kind of fraction throughout the day. I deal with numbers just about everywhere I go. Math has always been on my vocabulary since I was young. Coming from a house of five, I deal with math every single day. I have to use math for my bills, the rent, groceries, gas, things that are important in the house. Now that I completed eleven and half years in the united Stated Marine Corps, I deal with a tremendous budget in my house. I know that things are not the same because I don’t have a steady income coming in I have to keep track of our expenses and cut back on a lot of unimportant expenses. No matter what we do whether it’s at work, home, or out in town, numbers will always be a factor. Math will be involved and that’s the good think about life. Most people need a solid understanding for financial success and math is the answer. (Huebsch, 2009) In life, you will always have that percent that only need to learn numbers to a certain point. We engage numbers at a very young age. No one really knows how long numbers have been around for. Most people understand the concept of numbers, equations, and the use of daily concepts. (Melayu, 2009) I could say that Im that percentage in my in this world. I go to sleep thinking about numbers and I wake up think about fractions and percentages. That’s the beauty about math. It’s a never ending stoty. I use math at school. I have to...
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...A.D250 and continued to flourish for more than 600 years. The Maya produced remarkable architecture, paintings, pottery and sculpture. They made outstanding advancements in astronomy and mathematics and developed an accurate yearly calendar. Maya were also the first people in the Western Hemisphere to develop an advanced form of writing. Today, their territory is divided between Mexico and several Central American countries. Through this study, the researchers aim to have knowledge and ideas about them and to know their Mathematical system. In addition, researchers and students may find out that the research about Maya is an interesting topic because they will know how they predicted the past events in this world. Statement of the Problem This research aimed to know and share an idea that could enlighten the reader. Thus, this research sought to answer the following questions: 1. Who are the Maya? 2. What are their Calendar System and Numerals? 3. How did they predict the End of the World in 2012? 4. What are the other predictions predicted by the Maya? 5. How accurate was the predictions of the Maya in the past events? Significance of the Study Since we are now living in the modern age, some of the people who were born in this age might have not been aware about the past, and they might be curious about it. Other schools nowadays, taught us about histories from the past, but not all. Others don`t know who are the Maya. They are more focused on the topic...
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...The Importance of Number Sense in the Elementary Classroom Robyn Thomas EDU Instructor: Dr. Silvernail November 2, 2011 Abstract In today’s elementary classrooms, students are expected to think and speak on high levels of intelligence. Teachers are encouraged to set high expectations, to question and probe and to ask students to explain what they are thinking. This paper will focus on the importance of understanding numbers or possessing number sense at the elementary level. The idea that students should already have some number sense is controversial. Struggling students in today’s classroom in the area of math seem to lack a major concept, which is a basic math skill or understanding numbers. What is number sense? Number sense refers to a person's general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving complex problems. Number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. Most children acquire this conceptual structure informally through interactions with parents and siblings before they enter kindergarten (Marshall 2010) . Other children who have not acquired it require formal instruction to do so. For example, one child may enter school knowing that...
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... | Title of the Chapter I. Topic of First Main Section of the chapter (include definitions, explanations, details and page numbers) A. First Main Point under the First Main Section of the chapter (include definitions, explanations, details and page numbers) 1. Subpoint under the Main point a. Detail and/or definition for the subpoint 2. Subpoint under the Main point a. Detail and/or definition for the subpoint 3. Subpoint under the Main point a. Detail and/or definition for the subpoint B. Second Main Point under the First Main Section of the chapter (include definitions, explanations, details and page numbers) 1. Subpoint under the Main point a. Detail and/or definition for the subpoint 2. Subpoint under the Main point a. Detail and/or definition for the subpoint 3. Subpoint under the Main point a. Detail and/or definition for the subpoint C. Third Main Point under the First Main Section of the chapter (include definitions, explanations, details and page numbers) 1. Subpoint under the Main point a. Detail and/or definition for the subpoint 2. Subpoint under the Main point ...
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...cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume. Year-at-a-Glance Instructional Window 1 Unit 1.1: Expanding Understanding of Place Value and Decimals Unit 1.2: Comparing and Rounding Decimals Instructional Window 2 Unit 2.1: Adding and Subtracting Decimals Unit 2.2: Developing Multiplication and Division Strategies Instructional Window 3 Unit 3.1: Solving Problems including Volume Unit 3.1: Using Equivalency to Add and Subtract Fractions Instructional Window 4 Unit 4.1: Understanding the Concept of Multiplying Fractions by Fractions Unit 4.2: Developing the Concept of Dividing Unit Fractions Instructional Window 5 Unit 5.1: Classifying Two Dimensional Geometric Figures Unit 5.2: Exploring the Coordinate Plane Unit 5.3: Representing Algebraic Thinking Fluency and/or Culminating Standards 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. (Fluency standard will be assessed on PIA 5.) Copyright 2014 District of Columbia Government Grade 5 Overview OPERATIONS AND ALGEBRAIC THINKING o Write and interpret numerical expressions. o Analyze patterns and relationships. NUMBER AND OPERATIONS IN BASE TEN Understand...
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...Trident Pre-Baccalaureate Assessment The questions below will assess your knowledge of pre-requisite skills required for MAT 101. Please answer the questions honestly, without the use of outside resources. Doing so will help you determine what you need to review prior to enrolling in MAT 101. Do not use a calculator where stated. Transfer your answers to the Student Solution Worksheet using CAPITAL letters. It is recommended that you print out this assessment to keep track of your work and answers. If you do not know an answer, you can make a note next to the problem and skip it. This will help you determine which sections you need to review. (Domain 1: The Real Number System) 1. Simplify 4 – (-10) A. 6 B. 14 C. -14 D. -6 2. Simplify | -25| - |3| A. 28 B. -25 C. -28 D. 22 3. What are the factors of 12? A. 1 & 12 B. 2 & 6 C. 1, 2, 3, 4, 6, & 12 D. 2, 3, 4, & 6 4. What is the least common multiple of 5 and 18? A. 5 B. 18 C. 23 D. 90 5. What is the greatest common factor of 30 and 75? A. 150 B. 5 C. 15 D. 1 6. Simplify using the order of operations: 5* [32 + (9-5) * 23] - 1 A. 391 B. 204 C. 301 D. 164 (Domain 2: Operations with Fractions) 7. Write the fraction is simplest form. 24210 A. 12105 B. 652 C. 435 D. 18 8. Multiply the fractions and reduce to lowest terms if necessary. 25×109 A. 2045 ...
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...able to reduce the risk of those loose reports becoming misplaced and/or lost, which seems to make the most sense to me since this would be the best idea to prevent the loose reports from being misplaced and/or lost. However, the different sizes of facilities tend to organize patient files differently according to each particular facility’s policies. The most popular methods of organization that I have seen include chronologically, form numbers, report type, category and most recent. During my review of the interview threads, I have noticed a lot of similarities and a lot of differences in how patient files are organized between the many facilities which is leading me to believe that every facility has their own system. A system that may work for one facility does not work for another facility, especially when many facilities specialize in different medical areas. A small orthopedic facility may organize their patient’s files by last names where as a large hospital facility may organize their patient’s files by a numerical system they prefer and find to be the best...
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...Teaching Place Value Effectively Considering place value underpins all operations with number it is not difficult to understand the critical nature of children developing a robust understanding of this concept. As with all learning, place value is best understood and internalised by children when it is presented in real world contexts using materials, games and activities that build on and extend prior knowledge. A constructivist approach to learning that allows children an active role in developing knowledge is considered valuable as children build their own view of mathematics (Booker et al., 2014). Construction of a solid understanding of number and place value develops sequentially over many years through distinct stages: one digit numbers...
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