Mark Important Points in Margin. Significant Figures. Determine which digits in a number are significant.

Size: px
Start display at page:

Download "Mark Important Points in Margin. Significant Figures. Determine which digits in a number are significant."

Transcription

1 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 digits in a number are significant. Express the uncertainty of a measurement based on its significant digits. Round a number to the desired number of significant digits based on its precision. Perform mathematical calculations and round the answer to the correct number of significant figures. significant figures (also called significant digits): the digits whose value is known precisely; the digits that were measured. insignificant figures (also called insignificant digits): the digits that are part of the number, but whose values are not known; the digits that were rounded off or not measured. Chemistry I Page 1 of 7

2 Ideally, scientists would always write the value and the uncertainty for all numbers, but this is often impractical. A common shortcut is to express the precision of a measurement through rounding. E.g., the number 125,000 is clearly measured (or rounded off) to the nearest 1,000. If we were to write this number including its uncertainty, we would write 125,000 ± 1,000. The values of the hundreds, tens, and ones digits are not known, because they are beyond the precision of the measurement. If we were able to measure more precisely, the actual number would be between 124,000 and 126,000, and it would round off to 125,000. I.e., the number would most likely lie between 124,500 and 125, For the number 125,000 we would say that the first three digits are significant (the exact value is known), and the last three are insignificant (the exact value is unknown). For any measurement that does not have an explicitly stated uncertainty value, assume the uncertainty is ±1 in the last significant digit. Chemistry I Page 2 of 7

3 Identifying the in a Number The first significant digit is where the measured part of the number begins the first digit that is not zero. The last significant digit is the last measured digit the last digit whose true value is known or accurately estimated (usually ±1). If the number doesn t have a decimal point, the last significant digit will be the last digit that is not zero. If the number does have a decimal point, the last significant digit will be the last digit shown. If the number is in scientific notation, the above rules tell us (correctly) that all of the digits before the times sign are significant. In the following numbers, the significant figures have been underlined: 13, (note the decimal point at the end) Chemistry I Page 3 of 7

4 When Not to Use Significant Figues Significant figure rules only apply in situations where the numbers you are working with have a limited precision. This is usually the case when the numbers represent measurements. Exact numbers have infinite precision, and therefore have an infinite number of significant figures. Some examples of exact numbers are: Pure numbers, such as the ones you encounter in math class. Anything you can count. (E.g., there are 24 people in the room. That means exactly 24 people, not 24.0 ± 0.1 people.) Whole-number exponents in formulas. (E.g., the area of a circle is πr 2. This is an exact formula, so the 2 is exact.) What to Do When Rounding Doesn t Give the Correct Number of If you have a different number of significant digits from what the rounding shows, you can place a line over the last significant digit, or you can place the whole number in scientific notation. Both of the following have four significant digits, and both are equivalent to writing 13,000 ± , Chemistry I Page 4 of 7

5 Math with Whenever you do math with significant figures, the answer can t be more precise than the numbers that it came from. There are two simple rules to make sure this doesn t happen: Addition & Subtraction: Line up the numbers in a column. Any column that has an uncertain digit a zero from rounding is an uncertain column. (Uncertain digits are shown as question marks in the right column below.) You need to round off your answer to get rid of all of the uncertain columns. For example: problem: meaning: 23???.???? ?.???? 24???.???? Because we can t know which digits go in the hundreds, tens, ones, and decimal places of all of the addends, the exact values of those digits must therefore be unknown in the sum. This means we need to round off the answer to the nearest 1,000, which gives a final answer of 25,000 (which actually means 25,000 ± 1,000). A silly (but correct) example of addition with significant digits is: = 100 Chemistry I Page 5 of 7

6 Multiplication, Division, Etc. For multiplication, division, and just about everything else (except for addition and subtraction, which we have already discussed), round your answer off to the same number of significant digits as the number that has the fewest. For example, consider the problem = The number 1.4 has the fewest significant digits (2). Remember that 1.4 really means 1.4 ± 0.1. This means the actual value, if we had more precision, could be anything between 1.3 and 1.5. This means the actual answer could be anything between = and = This means the actual answer is ± This means that the ones digit is approximate, and everything beyond it is unknown. Therefore, it would make the most sense to report the number as 48 ± 3. In this problem, notice that the least significant term in the problem (1.4) had 2 significant digits, and the answer (48) also has 2 significant digits. This is where the rule comes from. A silly (but correct) example of multiplication with significant digits is: = 100 Chemistry I Page 6 of 7

7 Mixed Operations For mixed operations, keep all of the digits until you re finished (so roundoff errors don t accumulate), but keep track of the last significant digit in each step by putting a line over it (even if it s not a zero). Once you have your final answer, round it to the correct number of significant digits. Don t forget to use the correct order of operations (PEMDAS)! For example: ( ) + ( ) 7, = 7, = 7,400 Note that in the above example, we kept all of the digits until the end. This is to avoid introducing small rounding errors at each step, which can add up to enough to change the final answer. Notice how, if we had rounded off the numbers at each step, we would have gotten the wrong answer: ( ) + ( ) 7, = 7,3 10 = 7,300 When All Else Fails Significant figures are an approximation. With most lab equipment, it is only possible to make measurements to three digits of precision (two digits from the markings, plus one estimated digit). This means that most calculations will be rounded to 3 significant digits. Any time you re not sure how many significant digits you need, 3 is usually a pretty good guess. Chemistry I Page 7 of 7

Calculations with Sig Figs

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.,

More information

Significant Figures & Scientific Notation

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

More information

Rev Name Date. . Round-off error is the answer to the question How wrong is the rounded answer?

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

More information

Exponential Numbers ID1050 Quantitative & Qualitative Reasoning

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

More information

Significant Figures. For example. Let s try this one. Introduction to Significant Figures & Scientific Notation

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

More information

TOPIC 2 DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3

TOPIC 2 DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3 TOPIC DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3 Association between Fractions and Decimals is a fraction. It means divided by. If we divide by the result is not a whole number. It is a half of whole

More information

SECTION 3. ROUNDING, ESTIMATING, AND USING A CALCULATOR

SECTION 3. ROUNDING, ESTIMATING, AND USING A CALCULATOR SECTION 3. ROUNDING, ESTIMATING, AND USING A CALCULATOR Exact numbers are not always necessary or desirable. Sometimes it may be necessary to express the number which is a result of a calculation to a

More information

MA 1128: Lecture 02 1/22/2018

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

More information

Decimals. Chapter Five

Decimals. Chapter Five Chapter Five Decimals 5.1 Introductions to Decimals 5.2 Adding & Subtracting Decimals 5.3 Multiplying Decimals & Circumference of a Circle 5.4 Dividing Decimals 5.5 Fractions, Decimals, & Order of Operations

More information

!"!!!"!!"!! = 10!!!!!(!!) = 10! = 1,000,000

!!!!!!!! = 10!!!!!(!!) = 10! = 1,000,000 Math Review for AP Chemistry The following is a brief review of some of the math you should remember from your past. This is meant to jog your memory and not to teach you something new. If you find you

More information

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.) WHOLE NUMBERS REVIEW A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects (such as money,

More information

Appendix 1: REVIEW OF TREATMENT OF SIGNIFICANT FIGURES

Appendix 1: REVIEW OF TREATMENT OF SIGNIFICANT FIGURES Appendix 1: REVIEW OF TREATMENT OF SIGNIFICANT FIGURES PART I: HOW MANY DIGITS SHOULD YOU RECORD? When you measure an object with a ruler such as Ruler I shown in the figure below, you know for sure that

More information

Topic 2: Decimals. Topic 1 Integers. Topic 2 Decimals. Topic 3 Fractions. Topic 4 Ratios. Topic 5 Percentages. Topic 6 Algebra

Topic 2: Decimals. Topic 1 Integers. Topic 2 Decimals. Topic 3 Fractions. Topic 4 Ratios. Topic 5 Percentages. Topic 6 Algebra 41 Topic 2: Decimals Topic 1 Integers Topic 2 Decimals Topic 3 Fractions Topic 4 Ratios Duration 1/2 week Content Outline Introduction Addition and Subtraction Multiplying and Dividing by Multiples of

More information

Summer Assignment Glossary

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

More information

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number

More information

What is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole

What is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole // Fractions Pages What is a Fraction? Fraction Part of a Whole Top Number? Bottom Number? Page Numerator tells how many parts you have Denominator tells how many parts are in the whole Note: the fraction

More information

Adding and Subtracting with Decimals

Adding and Subtracting with Decimals Adding and Subtracting with Decimals Before you can add or subtract numbers with decimals, all the decimal points must be lined up. (It will help if you use zeros to fill in places so that the numbers

More information

Example 2: Simplify each of the following. Round your answer to the nearest hundredth. a

Example 2: Simplify each of the following. Round your answer to the nearest hundredth. a Section 5.4 Division with Decimals 1. Dividing by a Whole Number: To divide a decimal number by a whole number Divide as you would if the decimal point was not there. If the decimal number has digits after

More information

1.- DECIMAL PLACE VALUE: tenths, hundredths, thousandths. 1.1 Ordering decimals. 1.2 Rounding CALCULATIONS. 2.- ADDITION AND SUBTRACTION OF DECIMALS

1.- DECIMAL PLACE VALUE: tenths, hundredths, thousandths. 1.1 Ordering decimals. 1.2 Rounding CALCULATIONS. 2.- ADDITION AND SUBTRACTION OF DECIMALS 1 1.- DECIMAL PLACE VALUE: tenths, hundredths, thousandths. 1.1 Ordering decimals. 1.2 Rounding CALCULATIONS. 2.- ADDITION AND SUBTRACTION OF DECIMALS 3.- MULTIPLICATION AND DIVISION. 3.1 Multiplication

More information

Part B: Significant Figures = Precision

Part B: Significant Figures = Precision Part A: Accuracy vs. Precision The terms precision and accuracy are often used in discussing measured values. Precision is a measure of how closely individual measurements agree with one another or is

More information

Chapter 2: Measurement and Problem Solving

Chapter 2: Measurement and Problem Solving Chapter 2: Measurement and Problem Solving Determine which digits in a number are significant. Round numbers to the correct number of significant figures. Determine the correct number of significant figures

More information

Chapter 4 Section 2 Operations on Decimals

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.

More information

6.1 Evaluate Roots and Rational Exponents

6.1 Evaluate Roots and Rational Exponents VOCABULARY:. Evaluate Roots and Rational Exponents Radical: We know radicals as square roots. But really, radicals can be used to express any root: 0 8, 8, Index: The index tells us exactly what type of

More information

Exponential Notation

Exponential Notation Exponential Notation INTRODUCTION Chemistry as a science deals with the qualitative and quantitative aspects of substances. In the qualitative part, we deal with the general and specific properties of

More information

DECIMALS are special fractions whose denominators are powers of 10.

DECIMALS are special fractions whose denominators are powers of 10. Ch 3 DECIMALS ~ Notes DECIMALS are special fractions whose denominators are powers of 10. Since decimals are special fractions, then all the rules we have already learned for fractions should work for

More information

Divisibility Rules and Their Explanations

Divisibility Rules and Their Explanations Divisibility Rules and Their Explanations Increase Your Number Sense These divisibility rules apply to determining the divisibility of a positive integer (1, 2, 3, ) by another positive integer or 0 (although

More information

Gateway Regional School District VERTICAL ARTICULATION OF MATHEMATICS STANDARDS Grades K-4

Gateway Regional School District VERTICAL ARTICULATION OF MATHEMATICS STANDARDS Grades K-4 NUMBER SENSE & OPERATIONS K.N.1 Count by ones to at least 20. When you count, the last number word you say tells the number of items in the set. Counting a set of objects in a different order does not

More information

Significant Figure Rules

Significant Figure Rules Significant Figure Rules There are three rules on determining how many significant figures are in a number: 1. Non-zero digits are always significant. 2. Any zeros between two significant digits are significant.

More information

PIETRO, GIORGIO & MAX ROUNDING ESTIMATING, FACTOR TREES & STANDARD FORM

PIETRO, GIORGIO & MAX ROUNDING ESTIMATING, FACTOR TREES & STANDARD FORM PIETRO, GIORGIO & MAX ROUNDING ESTIMATING, FACTOR TREES & STANDARD FORM ROUNDING WHY DO WE ROUND? We round numbers so that it is easier for us to work with. We also round so that we don t have to write

More information

1.1 Review of Place Value

1.1 Review of Place Value 1 1.1 Review of Place Value Our decimal number system is based upon powers of ten. In a given whole number, each digit has a place value, and each place value consists of a power of ten. Example 1 Identify

More information

Topic C. Communicating the Precision of Measured Numbers

Topic C. Communicating the Precision of Measured Numbers Topic C. Communicating the Precision of Measured Numbers C. page 1 of 14 Topic C. Communicating the Precision of Measured Numbers This topic includes Section 1. Reporting measurements Section 2. Rounding

More information

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 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

More information

Parentheses ( ) Math Review. The Order of Operations tells us how to do a math problem with more than one operation, in the correct order.

Parentheses ( ) Math Review. The Order of Operations tells us how to do a math problem with more than one operation, in the correct order. Problem Solving in Chemistry Math Review We are faced with problems each day, and not just in chemistry A solution (answer) needs to be found Trial and Error may work sometimes but, there is a method to

More information

Get to Know Your Calculator!

Get to Know Your Calculator! Math BD Calculator Lab Name: Date: Get to Know Your Calculator! You are allowed to use a non-graphing, scientific calculator for this course. A scientific calculator is different from an ordinary hand-held

More information

ROUNDING ERRORS LAB 1. OBJECTIVE 2. INTRODUCTION

ROUNDING ERRORS LAB 1. OBJECTIVE 2. INTRODUCTION ROUNDING ERRORS LAB Imagine you are traveling in Italy, and you are trying to convert $27.00 into Euros. You go to the bank teller, who gives you 20.19. Your friend is with you, and she is converting $2,700.00.

More information

Repeat or Not? That Is the Question!

Repeat or Not? That Is the Question! Repeat or Not? That Is the Question! Exact Decimal Representations of Fractions Learning Goals In this lesson, you will: Use decimals and fractions to evaluate arithmetic expressions. Convert fractions

More information

Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 10.

Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 10. PA Ch 5 Rational Expressions Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 0. Since decimals are special

More information

8/30/2016. In Binary, We Have A Binary Point. ECE 120: Introduction to Computing. Fixed-Point Representations Support Fractions

8/30/2016. In Binary, We Have A Binary Point. ECE 120: Introduction to Computing. Fixed-Point Representations Support Fractions University of Illinois at Urbana-Champaign Dept. of Electrical and Computer Engineering ECE 120: Introduction to Computing Fixed- and Floating-Point Representations In Binary, We Have A Binary Point Let

More information

Excerpt from "Art of Problem Solving Volume 1: the Basics" 2014 AoPS Inc.

Excerpt from Art of Problem Solving Volume 1: the Basics 2014 AoPS Inc. Chapter 5 Using the Integers In spite of their being a rather restricted class of numbers, the integers have a lot of interesting properties and uses. Math which involves the properties of integers is

More information

KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS

KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS DOMAIN I. COMPETENCY 1.0 MATHEMATICS KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS Skill 1.1 Compare the relative value of real numbers (e.g., integers, fractions, decimals, percents, irrational

More information

(Refer Slide Time: 02:59)

(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

More information

Floating-Point Numbers in Digital Computers

Floating-Point Numbers in Digital Computers POLYTECHNIC UNIVERSITY Department of Computer and Information Science Floating-Point Numbers in Digital Computers K. Ming Leung Abstract: We explain how floating-point numbers are represented and stored

More information

Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions

Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions Variable is a letter or symbol that represents a number. Variable (algebraic)

More information

Floating-Point Numbers in Digital Computers

Floating-Point Numbers in Digital Computers POLYTECHNIC UNIVERSITY Department of Computer and Information Science Floating-Point Numbers in Digital Computers K. Ming Leung Abstract: We explain how floating-point numbers are represented and stored

More information

add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) I created these worksheets because I think it is useful to have regular practice of calculation methods away from the point of teaching. There are worksheets. Questions are aligned to the Year curriculum,

More information

1.3.B Significant Figures

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

More information

Section 0.3 The Order of Operations

Section 0.3 The Order of Operations Section 0.3 The Contents: Evaluating an Expression Grouping Symbols OPERATIONS The Distributive Property Answers Focus Exercises Let s be reminded of those operations seen thus far in the course: Operation

More information

CIV Module Unit Session Learning Objectives

CIV Module Unit Session Learning Objectives CIV Module Unit Session Learning Objectives C IV Module: Essentials of Recognizing a Fraction 1. Learning that a fraction is a part of a whole through the use of area models C IV Module: Essentials of

More information

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology Intermediate Algebra Gregg Waterman Oregon Institute of Technology c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license

More information

Math 6 Notes Unit 03 Notes: Decimals

Math 6 Notes Unit 03 Notes: Decimals Math 6 Notes Unit 03 Notes: Decimals Reading and Writing Decimals Syllabus Objective: (3.2) The student will translate written forms of fractions, decimals, and percents to numerical form. Decimals are

More information

Measurements: Significant Figures

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

More information

1.3 Floating Point Form

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

More information

UNIT 6 OPERATIONS WITH DECIMALS

UNIT 6 OPERATIONS WITH DECIMALS UNIT 6 OPERATIONS WITH DECIMALS INTRODUCTION In this Unit, we will use our understanding of operations, decimals, and place value to perform operations with decimals. The table below shows the learning

More information

Step 1 The number name given in the question is five and sixty-eight-hundredths. We know that

Step 1 The number name given in the question is five and sixty-eight-hundredths. We know that Answers (1) 5.68 The number name given in the question is five and sixty-eight-hundredths. We know that hundredths can be represented as 1. So, we can write five and sixty-eight-hundredths as 5 and 68

More information

Scientific notation. Complete the chart below x x x What time is it?

Scientific notation. Complete the chart below x x x What time is it? Homework Answers p.148 #6 and #7 Express as decimal: 6a) 4.83 x 10 2 = 483 b) 7.221 x 10-4 = 0.0007221 c) 6.1x 10 0 = 6.1 Put in standard scien?fic nota?on: 7a) 142.3 x 10 3 = 1.423 x 10 5 b) 0.0007741

More information

SAMLab Tip Sheet #1 Translating Mathematical Formulas Into Excel s Language

SAMLab Tip Sheet #1 Translating Mathematical Formulas Into Excel s Language Translating Mathematical Formulas Into Excel s Language Introduction Microsoft Excel is a very powerful calculator; you can use it to compute a wide variety of mathematical expressions. Before exploring

More information

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6 NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our

More information

Lesson 1: THE DECIMAL SYSTEM

Lesson 1: THE DECIMAL SYSTEM Lesson 1: THE DECIMAL SYSTEM The word DECIMAL comes from a Latin word, which means "ten. The Decimal system uses the following ten digits to write a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each time

More information

Grade 4 Math Proficiency Scales-T1

Grade 4 Math Proficiency Scales-T1 Measurement & Data Geometry Critical Thinking Communication Grade 4 Math Proficiency Scales-T1 Novice 1 and of the Make mathematical arguments and critique the reasoning of others. Partially Proficient

More information

Unit 1 Numbers and Algebra Study Guide

Unit 1 Numbers and Algebra Study Guide Name Date Unit 1 Study Guide Unit 1 Numbers and Algebra Study Guide In this unit, you were introduced to some basic elements and concepts of mathematics. Mastery of this section is necessary in order to

More information

Chapter 03: Computer Arithmetic. Lesson 09: Arithmetic using floating point numbers

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

More information

Grades 7 & 8, Math Circles 31 October/1/2 November, Graph Theory

Grades 7 & 8, Math Circles 31 October/1/2 November, Graph Theory Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grades 7 & 8, Math Circles 31 October/1/2 November, 2017 Graph Theory Solutions Example 1 1. To represent

More information

Lesson 6: Manipulating Equations

Lesson 6: Manipulating Equations Lesson 6: Manipulating Equations Manipulating equations is probably one of the most important skills to master in a high school physics course. Although it is based on familiar (and fairly simple) math

More information

Math 340 Fall 2014, Victor Matveev. Binary system, round-off errors, loss of significance, and double precision accuracy.

Math 340 Fall 2014, Victor Matveev. Binary system, round-off errors, loss of significance, and double precision accuracy. Math 340 Fall 2014, Victor Matveev Binary system, round-off errors, loss of significance, and double precision accuracy. 1. Bits and the binary number system A bit is one digit in a binary representation

More information

2.2 Scientific Notation & Dimensional Analysis. Monday, September 23, 13

2.2 Scientific Notation & Dimensional Analysis. Monday, September 23, 13 2.2 Scientific Notation & Dimensional Analysis Scientific Notation Can be used to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to any power (exponent). 36,000 =

More information

REVIEW OF BASIC MATHEMATICAL CONCEPTS

REVIEW OF BASIC MATHEMATICAL CONCEPTS REVIEW OF BASIC MATHEMATICAL CONCEPTS The following document is a modified version of a laboratory exercise prepared for students taking general biology. It is provided here for individual review purposes

More information

Decimal Binary Conversion Decimal Binary Place Value = 13 (Base 10) becomes = 1101 (Base 2).

Decimal Binary Conversion Decimal Binary Place Value = 13 (Base 10) becomes = 1101 (Base 2). DOMAIN I. NUMBER CONCEPTS Competency 00 The teacher understands the structure of number systems, the development of a sense of quantity, and the relationship between quantity and symbolic representations.

More information

MAT 003 Brian Killough s Instructor Notes Saint Leo University

MAT 003 Brian Killough s Instructor Notes Saint Leo University MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample

More information

Signed umbers. Sign/Magnitude otation

Signed umbers. Sign/Magnitude otation Signed umbers So far we have discussed unsigned number representations. In particular, we have looked at the binary number system and shorthand methods in representing binary codes. With m binary digits,

More information

Math 6 Unit 2: Understanding Number Review Notes

Math 6 Unit 2: Understanding Number Review Notes Math 6 Unit 2: Understanding Number Review Notes Key unit concepts: Use place value to represent whole numbers greater than one million Solve problems involving large numbers, using technology Determine

More information

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. 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

More information

Math 6, Unit 1 Notes: Whole Numbers Estimating, and Patterns

Math 6, Unit 1 Notes: Whole Numbers Estimating, and Patterns Math 6, Unit 1 Notes: Whole Numbers Estimating, and Patterns Objectives: (1.2) The student will estimate by rounding to a given place value. (1.5) The student will use a variety of methods to estimate.

More information

Chapter 1 Operations With Numbers

Chapter 1 Operations With Numbers Chapter 1 Operations With Numbers Part I Negative Numbers You may already know what negative numbers are, but even if you don t, then you have probably seen them several times over the past few days. If

More information

fractional quantities are typically represented in computers using floating point format this approach is very much similar to scientific notation

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

More information

Rules for deciding the number of significant figures in a measured quantity:

Rules for deciding the number of significant figures in a measured quantity: Rules for deciding the number of significant figures in a measured quantity: (1) All nonzero digits are significant: 1.234 g has 4 significant figures, 1.2 g has 2 significant figures. (2) Zeroes between

More information

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.) 1, etc.. π, 2, 3, etc.. SECTION 1.1 A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects

More information

NUMBERS AND NUMBER RELATIONSHIPS

NUMBERS AND NUMBER RELATIONSHIPS MODULE MODULE CHAPTERS Numbers and number patterns 2 Money matters KEY SKILLS writing rational numbers as terminating or recurring decimals identifying between which two integers any irrational number

More information

EXCEL PRACTICE 5: SIMPLE FORMULAS

EXCEL PRACTICE 5: SIMPLE FORMULAS EXCEL PRACTICE 5: SIMPLE FORMULAS SKILLS REVIEWED: Simple formulas Printing with and without formulas Footers Widening a column Putting labels and data in Bold. PART 1 - DIRECTIONS 1. Open a new spreadsheet

More information

CHAPTER 4: DECIMALS. Image from Microsoft Office Clip Art CHAPTER 4 CONTENTS

CHAPTER 4: DECIMALS. Image from Microsoft Office Clip Art CHAPTER 4 CONTENTS CHAPTER 4: DECIMALS Image from Microsoft Office Clip Art CHAPTER 4 CONTENTS 4.1 Introduction to Decimals 4.2 Converting between Decimals and Fractions 4.3 Addition and Subtraction of Decimals 4.4 Multiplication

More information

Algebra 2 Semester 1 (#2221)

Algebra 2 Semester 1 (#2221) Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the 2016-2017 Course Guides for the following course: Algebra 2 Semester

More information

Computer Numbers and their Precision, I Number Storage

Computer Numbers and their Precision, I Number Storage Computer Numbers and their Precision, I Number Storage Learning goal: To understand how the ways computers store numbers lead to limited precision and how that introduces errors into calculations. Learning

More information

Common Core State Standards Mathematics (Subset K-5 Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base 10)

Common Core State Standards Mathematics (Subset K-5 Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base 10) Kindergarten 1 Common Core State Standards Mathematics (Subset K-5 Counting and Cardinality,, Number and Operations in Base 10) Kindergarten Counting and Cardinality Know number names and the count sequence.

More information

Learn Ninja-Like Spreadsheet Skills with LESSON 9. Math, Step by Step

Learn Ninja-Like Spreadsheet Skills with LESSON 9. Math, Step by Step EXCELL MASTERY Learn Ninja-Like Spreadsheet Skills with LESSON 9 Doing Math, Step by Step It s Elementary, My Dear Ninja There is a scene in the short story The Crooked Man, where Sherlock Holmes accurately

More information

Dr. Yau s Math Review for General Chemistry I

Dr. Yau s Math Review for General Chemistry I Dr. Yau s Math Review for eneral Chemistry I The following is a brief review of some of the math you should remember from your past. This is meant to jog your memory and not to teach you something new.

More information

Is the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd

Is the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd Is the statement sufficient? If both x and y are odd, is xy odd? Is x < 0? 1) xy 2 < 0 Positives & Negatives Answer: Yes, xy is odd Odd numbers can be represented as 2m + 1 or 2n + 1, where m and n are

More information

Revision on fractions and decimals

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

More information

Here are some of the more basic curves that we ll need to know how to do as well as limits on the parameter if they are required.

Here are some of the more basic curves that we ll need to know how to do as well as limits on the parameter if they are required. 1 of 10 23/07/2016 05:15 Paul's Online Math Notes Calculus III (Notes) / Line Integrals / Line Integrals - Part I Problems] [Notes] [Practice Problems] [Assignment Calculus III - Notes Line Integrals Part

More information

Converting Between Mixed Numbers & Improper Fractions

Converting Between Mixed Numbers & Improper Fractions 01 Converting Between Mixed Numbers & Improper Fractions A mixed number is a whole number and a fraction: 4 1 2 An improper fraction is a fraction with a larger numerator than denominator: 9 2 You can

More information

Prefix/Infix/Postfix Notation

Prefix/Infix/Postfix Notation Prefix/Infix/Postfix Notation One commonly writes arithmetic expressions, such as 3 + 4 * (5-2) in infix notation which means that the operator is placed in between the two operands. In this example, the

More information

Comp 151. More on Arithmetic and intro to Objects

Comp 151. More on Arithmetic and intro to Objects Comp 151 More on Arithmetic and intro to Objects Admin Any questions 2 The Project Lets talk about the project. What do you need A 'accumulator' variable. Start outside of the loop Lets look at your book's

More information

I can use number bonds and matching subtraction facts up to 20.

I can use number bonds and matching subtraction facts up to 20. Year 1, Maths end of year expectations I can count to and past 100. Forwards and backwards starting from any number. I can count, read and write numbers to 100 in numerals and count in jumps of 2, 5 and

More information

THE REAL NUMBER SYSTEM

THE REAL NUMBER SYSTEM THE REAL NUMBER SYSTEM Review The real number system is a system that has been developing since the beginning of time. By now you should be very familiar with the following number sets : Natural or counting

More information

COMPETENCY 1.0 UNDERSTAND THE STRUCTURE OF THE BASE TEN NUMERATION SYSTEM AND NUMBER THEORY

COMPETENCY 1.0 UNDERSTAND THE STRUCTURE OF THE BASE TEN NUMERATION SYSTEM AND NUMBER THEORY SUBAREA I. NUMBERS AND OPERATIONS COMPETENCY.0 UNDERSTAND THE STRUCTURE OF THE BASE TEN NUMERATION SYSTEM AND NUMBER THEORY Skill. Analyze the structure of the base ten number system (e.g., decimal and

More information

2.Simplification & Approximation

2.Simplification & Approximation 2.Simplification & Approximation As we all know that simplification is most widely asked topic in almost every banking exam. So let us try to understand what is actually meant by word Simplification. Simplification

More information

Section 1.4 Mathematics on the Computer: Floating Point Arithmetic

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

More information

Watkins Mill High School. Algebra 2. Math Challenge

Watkins Mill High School. Algebra 2. Math Challenge Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking

More information

Real Numbers. Rational Numbers (0, 3, -1, ½⅔,.524, etc..) Fractions (1/2, -4/3, 10%,.25, etc..) Negative Integers {.

Real Numbers. Rational Numbers (0, 3, -1, ½⅔,.524, etc..) Fractions (1/2, -4/3, 10%,.25, etc..) Negative Integers {. All Numbers in the Universe Real Numbers Imaginary Numbers 1, etc.. Rational Numbers (0, 3, -1, ½⅔,.524, etc..) Irrational Numbers, 2, 3, etc.. Integers (.-3,-2,-1,0,1,2,3..) Fractions (1/2, -4/3, %,.25,

More information

A) Decimal Notation and Writing Decimals in Words. ecim B) Writing Decimals in Standard Form.

A) Decimal Notation and Writing Decimals in Words. ecim B) Writing Decimals in Standard Form. 5.1 Introduction to Decimals A) Decimal Notation and Writing Decimals in Words. Decimals The Place Value System for Decimal Numbers Tens/ ones/ decimal point/ tenths/ hundredths/ thousandths/ ten-thousandths

More information

DOWNLOAD PDF MICROSOFT EXCEL ALL FORMULAS LIST WITH EXAMPLES

DOWNLOAD PDF MICROSOFT EXCEL ALL FORMULAS LIST WITH EXAMPLES Chapter 1 : Examples of commonly used formulas - Office Support A collection of useful Excel formulas for sums and counts, dates and times, text manipularion, conditional formatting, percentages, Excel

More information