Physics 12 Rules for Significant Digits and Rounding

Size: px
Start display at page:

Download "Physics 12 Rules for Significant Digits and Rounding"

Transcription

1 1 Physics 12 Rules for Significant Digits and Rounding One mathematical aspect of problem-solving in the physical sciences that gives some students difficulty deals with the rounding of computed numerical values. Why we need to follow a set of rules for rounding off computed answers arises from the fact that every measured value contains an amount of uncertainty, meaning that no measured value is exact. When we do calculations with measured values, this uncertainty must be expressed in the final calculated value we obtain. There are a number of methods of expressing uncertainty in computed answers. The method that is most commonly used is the method of Significant Digits and Rounding. I am of the habit of using the term significant figures instead of significant digits. In every measured value, the significant figures include all the certain digits plus one digit that is uncertain. Identifying the digits in a measured value that are significant is the first step in learning to round-off computed values correctly. NOTE: THESE RULES APPLY ONLY TO MEASURED VALUES. NUMERIC VALUES THAT ARE PRESENT IN MATHEMATICAL EQUATIONS AND COUNTED VALUES ARE CONSIDERED TO BE EXACT AND THUS CONTAIN NO UNCERTAINTY. Identifying Significant Digits There are 5 rules for identifying significant digits in a measured value. Four of these rules involve zeros. Rule 1: All non-zero digits are significant s 3 significant figures 42 m 2 significant figures ( s is the symbol for seconds, m is the symbol for metres) Rule 2: Zeros between non-zero digits are significant. 102 m 3 significant figures 4003 s 4 significant figures Rule 3: Zeros at the end of a measured value that contains a decimal portion are significant m 4 significant figures 1.00 s 3 significant figures

2 2 Rule 4: Zeros at the front of a measured value are not significant. Such zeros are merely decimal place holders s 2 significant figures (the 5 and the 8) m 3 significant figures (the 2, the 6, and the last 0) If you find you are uncertain if such zeros are significant or not, rewrite the value in scientific notation. When you do so, the zeros at the front of the value disappear. If we rewrite the above examples in scientific notation, we get: 5.8 x 10-2 m 2.60 x 10-3 s Rule 5: Zeros at the end of a whole number measured value may or may not be significant. Example: 1400 m This could have 2, 3 or 4 significant figures How do we determine the actual number of significant figures in the above value? The only way to be absolutely certain how many of the digits are significant is to ask the person who made the measurement. If that person had rounded the measure to the nearest hundred metres, then only the 1 and the 4 are significant. If the measure was rounded to the nearest ten metres, then the 1, the 4, and the first 0 are significant. If the person rounded to the nearest one metre, then all four digits are significant. Because the significance of the two zeros in the above value is uncertain, such zeros are called ambiguous zeros. In a perfect world, one should not encounter ambiguous zeros. To indicate the significance of zeros at the end of a whole number measure, scientific notation should be used. To properly illustrate the number of significant digits in the above value, the person should have recorded the value in one of the following ways: 1.4 x 10 3 m if only 2 significant figures 1.40 x 10 3 m if 3 significant figures x 10 3 m if 4 significant figures So what does one do if ambiguous zeros are encountered? If no statement to the contrary is made, you MAY assume that all ambiguous zeros are NOT significant. However, in this course, I prefer that you use Don s Rule for Ambiguous Zeros: If you encounter a measured value with one ambiguous zero, assume it IS significant. If you encounter a measured value with two or more ambiguous zeros, assume that the FIRST ONE IS SIGNIFICANT AND THE REST ARE NOT.

3 3 Some textbooks will explicitly state something like: All zeros not clearly significant shall be taken as significant. Many textbooks avoid the use of scientific notation because it is more expensive to typeset and print values with scientific notation. Now that the rules for identifying significant figures has been established, we can examine how these rules are applied to the rounding of calculated values. There are two rules that must be applied; one for addition and subtraction, the other for multiplication and division. The Precision Rule: The first rule to be examined applies to addition and subtraction. There are different ways of defining precision. One definition states that precision is a measure of how closely two or more measures of some quantity correspond. This definition is usually applied to experimentally determined measures of some value. A second definition (my own) is this: When comparing measured values, the value that has its last significant figure in the smallest numerical place value is the more precise measure. This definition of precision may only be applied to two measures of the same type of quantity. That is, we apply when comparing two measures of length, or two measures of mass, or two measures of volume, etc. Given two measures of time such as 21.0 s and 2.48 s, the latter measure is more precise as its final significant figures (the 8), falls in the hundredths place whereas the final significant figure in the other value (the 0) falls in the tenths place. The Precision Rule states that when we add or subtract two or more values, their sum or difference must be rounded to the precision of the least precise value involved s s = s = 23.5 s The sum of the two numbers had to be rounded to the tenths place because the less precise value (21.0 s) is precise only to the tenths place. The other value is precise to the hundredths place m m 16.2 m = m = 121 m The final answer to the above calculation had to be rounded to the ones place as the least precise value (135 m) is precise only to the ones place. The other two values are precise to the tenths place.

4 4 The Accuracy Rule: The second rule to be examined applies to multiplication and division. There are different ways of defining accuracy. One definition states that accuracy is a measure of how closely a value corresponds to an accepted given value. This definition is usually applied to experimentally determined values. For example, if we performed an experiment to determine the speed of light, the accuracy of the result would be determined by how closely that result matches the actual speed of which happens to be 3.00 x 10 8 m/s (to 3 significant digits). A second definition (my own) is this: When comparing measured values, the one possessing the greater number of significant figures is the more accurate measure. This definition may be used when comparing any measured values, not just measures of the same type of quantity. For example, if you are told that the distance to the Sun is 1.50 x m and that it takes light 5.0 x 10 2 s for light from the Sun to reach us, the measure of the distance to the Sun is a more accurate measure as it has 3 significant figures while the given measure of time has only 2 significant figures. The Accuracy Rule tells us that when we multiply or divide two or more values, the final computed answer must be rounded to the accuracy of the least accurate value involved in the calculation m m x 10 m/s 4.65 s s The answer to the division above had to be rounded to 2 significant figures because the least accurate value (0.28 m) has only 2 significant figures. The more accurate value (4.65 s) has 3 significant figures s x m/s = m = 3.51 m The answer to the multiplication above had to be rounded to 3 significant digits because the least accurate value ( s) has only 3 significant digits. The more accurate value (142.5 m/s) has 4 significant digits. Clear as mud? Good. Here are a couple more rules.

5 5 When Do We Do the Rounding Off? It is VERY important that only final calculated values be rounded off. What this means is that when you do multi-step calculations, intermediate values are not rounded off before being used in subsequent calculation steps. If you need to write down an intermediate value for some reason, you can either write down ALL the digits in your calculator display, or write down a good number of them and store the value somewhere in your calculator s memory. If your calculator does not have more than one place to store values, it is inferior and should be replaced with something that cost more than $8. What this also means is that you may have to go through and analyze each step in a multi-step calculation to determine where to round your final answer. Example: A pendulum completes exactly 15 oscillations (swings) in 13.4 s. Determine: a) the period of the pendulum s oscillations, and, b) the number of oscillations completed in 37 s. Solution: a) Before we begin, please note that the equations used to solve this example will be developed later in this course. For now, just study the treatment of significant figures and rounding. Number of oscillations: n = 15 Length of the time interval, t = 13.4 s Period, T =? Period, T = t n s s The ellipses (the ) indicates that the answer to the above calculation has more digits. According to the accuracy rule tells us that the above answer must be rounded to 3 significant figures due to the fact that the measured value of time (13.4 s) has 3 significant figures. The number of oscillations (15) is an exact counted value, so it does not enter into the discussion of rounding. The correct rounded answer is s. b) Using the equation above, we can solve for the number of oscillations completed in 37 s. Length of the time interval, t = 37 s Period, T = s Number of oscillations: n =? n t T 37 s s oscillations

6 6 In the above calculation, both of the values used have two significant figures, so our answer must be rounded to 41 oscillations. While the value used for the period is the unrounded value, this value only has two significant figures as explained above. In the above calculation, we needed to use the unrounded value of the period to avoid roundoff error. If one were to use 0.89 s for the value of the period, the calculated answer would come out to This value would round up to 42, which is incorrect. The Odd/Even Rule for Rounding Values Ending in a 5: An obscure and seldom necessary rule to remember involves rounding calculated values ending exactly with the number 5. For example, if we performed the following calculation: Speed, v = 1.23 m 2.0 s = m/s According to the accuracy rule, the answer to the above calculation must be rounded to 2 significant figures. The final rounded answer is, therefore, 0.62 m/s. If the distance were longer, say, 12.5 m the calculation is: Speed, v = 1.25 m 2.0 s = m/s Again, the accuracy rule tells us to round this answer to 2 significant figures. Is the answer 0.63 m/s? NO!!!! Reason: the odd/even rule of 5 s. Some textbooks employ a rule that usually applies only to Pure Chemists (as far as I have seen, anyways). Here it is: For calculated values ending with a 5, we round up if the digit in front of the 5 is odd. If the digit in front of the 5 is even, the 5 is dropped. Note: this rule applies only to calculated values ending exactly with a 5 and nothing after the 5 AND when the place value where rounding occurs is immediately in front of that 5. Thus, if we wish to round the value to 2 significant digits, it becomes 6.3. It is incorrect to extend this rule in the following way: Since the number after the 2 is a 5, and 2 is an even number, we drop the 5 This reasoning is incorrect because the number does not end exactly with a 5.

7 7 If we wish to round the value to 2 significant figures, it becomes 6.1. It is incorrect to extend this rule in the following way: Since the number ends with a value after the 5, the 4 rounds up to give us Since the number in front of the 5 we now have is odd, it rounds up and we get 6.2 This reasoning is incorrect because the place value where the rounding occurs (the tenths place) is not immediately in front of the 5 in the calculated value. Many of the assignment and test questions used in this course were taken from past Provincial Exams. The question writers were not consistent with their use of the rule of 5 s. Be aware that it may be used in some of the questions you encounter. I would prefer if you DID NOT use this rule in this course. Now the good news! The Old Provincial Exam Specifications stated that all correct calculated answers rounded to 2 or 3 significant digits shall be considered fully correct. As such, all I ask is that you round your calculated answers to 2 or 3 significant digits. One significant digit will not be accepted as being correct. Nor shall 4 or more significant digits be accepted as being correct. Every error will cost you 0.5 marks.

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield LECSS Physics 11 Introduction to Physics and Math Methods 1 Physics 11 Introduction to Physics and Math Methods In this introduction, you will get a more in-depth overview of what Physics is, as well as

More information

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer.

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer. Summer Packet th into 6 th grade Name Addition Find the sum of the two numbers in each problem. Show all work.. 62 2. 20. 726 + + 2 + 26 + 6 6 Decimal Addition: Remember to line up the decimals before

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

Significant Figures. Significant Figures 18/02/2015. A significant figure is a measured or meaningful digit.

Significant Figures. Significant Figures 18/02/2015. A significant figure is a measured or meaningful digit. Significant Figures When counting objects, it is easy to determine the EXACT number of objects. Significant Figures Unit B1 But when a property such as mass, time, volume, or length is MEASURED, you can

More information

Summer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4.

Summer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4. Summer Math Packet for Students Entering 6th Grade Please have your student complete this packet and return it to school on Tuesday, September. Work on your packet gradually. Complete one to two pages

More information

Scientific Measurement

Scientific Measurement Scientific Measurement Sprint times are often measured to the nearest hundredth of a second (0.01 s). Chemistry also requires making accurate and often very small measurements. CHEMISTRY & YOU How do you

More information

Liquid-in-glass thermometer

Liquid-in-glass thermometer Liquid-in-glass thermometer Objectives The objective of this experiment is to introduce some basic concepts in measurement, and to develop good measurement habits. In the first section, we will develop

More information

13. [Place Value] units. The digit three places to the left of the decimal point is in the hundreds place. So 8 is in the hundreds column.

13. [Place Value] units. The digit three places to the left of the decimal point is in the hundreds place. So 8 is in the hundreds column. 13 [Place Value] Skill 131 Understanding and finding the place value of a digit in a number (1) Compare the position of the digit to the position of the decimal point Hint: There is a decimal point which

More information

Prepared by Sa diyya Hendrickson. Package Summary

Prepared by Sa diyya Hendrickson. Package Summary Introduction Prepared by Sa diyya Hendrickson Name: Date: Package Summary Defining Decimal Numbers Things to Remember Adding and Subtracting Decimals Multiplying Decimals Expressing Fractions as Decimals

More information

Q 1 Find the square root of 729. 6. Squares and Square Roots Q 2 Fill in the blank using the given pattern. 7 2 = 49 67 2 = 4489 667 2 = 444889 6667 2 = Q 3 Without adding find the sum of 1 + 3 + 5 + 7

More information

EXPERIMENT MEASUREMENT

EXPERIMENT MEASUREMENT PHYS 1401 General Physics I EXPERIMENT 1 MEASUREMENT and UNITS I. OBJECTIVE The objective of this experiment is to become familiar with the measurement of the basic quantities of mechanics and to become

More information

Numbers and Data Analysis

Numbers and Data Analysis Numbers and Data Analysis With thanks to George Goth, Skyline College for portions of this material. Significant figures Significant figures (sig figs) are only the first approimation to uncertainty and

More information

THE GRAMMAR AND ETIQUETTE OF SCIENTIFIC MATH

THE GRAMMAR AND ETIQUETTE OF SCIENTIFIC MATH THE GRAMMAR AND ETIQUETTE OF SCIENTIFIC MATH You can be a mathematician without a lot of science However, you can t be a scientist without math T.Webb HHS Part 1 - Terminology in Basic Data Analysis Quantitative

More information

1 Measurement Uncertainties

1 Measurement Uncertainties 1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.

More information

Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section C

Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section C Section C.1: Significant Digits Significant digits The digits in a number that represents actual measurements and therefore have meaning are called significant digits. Significant digits: Nonzero digits.

More information

Group 1 Group 2. 1 meter = 100 cm 9.88 cm of Copper Wire 1 dollar = 4 quarters Room Temp is 22.7 C

Group 1 Group 2. 1 meter = 100 cm 9.88 cm of Copper Wire 1 dollar = 4 quarters Room Temp is 22.7 C NAME: DUE DATE: JUNE 11 TH AP Chemistry SUMMER REV: Sig Figs Why? The number of digits (significant figures) reported for a measured value conveys the quality of the measurement and hence, the quality

More information

Appendix A: Significant Figures and Error Analysis

Appendix A: Significant Figures and Error Analysis 1 Appendix A: Significant Figures and Error Analysis Every measurement of a physical quantity contains some amount of uncertainty or error. We often speak of a certain number or measurement as being precise

More information

PHY131H1F Class 3. From Knight Chapter 1:

PHY131H1F Class 3. From Knight Chapter 1: PHY131H1F Class 3 Today: Error Analysis Significant Figures Unit Conversion Normal Distribution Standard Deviation Reading Error Propagation of Errors Error in the Mean From Knight Chapter 1: 1 Significant

More information

SIGNIFICANT FIGURES. x 100%

SIGNIFICANT FIGURES. x 100% Page 1 SIGNIFICANT FIGURES ASSIGNED READING: Zumdahal, et.al, Chemistry (10 th ed.), Chapter 1, Sec. 4 and 5. I. Accuracy and Precision It is important to remember, here at the outset of this course, that

More information

Liquid-in-glass thermometer

Liquid-in-glass thermometer Objectives Liquid-in-glass thermometer The objectives of this experiment is to introduce some basic concepts in measurement, and to develop good measurement habits. In the first section, we will develop

More information

Journal of Geoscience Education, v. 46, n. 3, p , May 1998 (edits, June 2005)

Journal of Geoscience Education, v. 46, n. 3, p , May 1998 (edits, June 2005) Journal of Geoscience Education, v. 46, n. 3, p. 292-295, May 1998 (edits, June 2005) Computational Geology 1 Significant Figures! H.L. Vacher, Department of Geology, University of South Florida, 4202

More information

Math Review for Chemistry

Math Review for Chemistry Chemistry Summer Assignment 2018-2019 Chemistry Students A successful year in Chemistry requires that students begin with a basic set of skills and knowledge that you will use the entire year. The summer

More information

A. Incorrect! Check your algebra when you solved for volume. B. Incorrect! Check your algebra when you solved for volume.

A. Incorrect! Check your algebra when you solved for volume. B. Incorrect! Check your algebra when you solved for volume. AP Chemistry - Problem Drill 03: Basic Math for Chemistry No. 1 of 10 1. Unlike math problems, chemistry calculations have two key elements to consider in any number units and significant figures. Solve

More information

AP PHYSICS 1 SUMMER PREVIEW

AP PHYSICS 1 SUMMER PREVIEW AP PHYSICS 1 SUMMER PREVIEW Name: Your summer homework assignment is to read through this summer preview, completing the practice problems, and completing TASK 1 and Task 2. It is important that you read

More information

Advanced Physics Summer Assignment.

Advanced Physics Summer Assignment. Advanced Physics Summer Assignment. Part 1 - Review /Read through the notes provided. Part 2 Assignment: Complete the math assignment sections that follow the notes. Metric Units & Conversion Multiplier

More information

Measurement 4: Scientific Notation

Measurement 4: Scientific Notation Q Skills Review The Decimal System Measurement 4: Scientific Notation Dr. C. Stewart We are so very familiar with our decimal notation for writing numbers that we usually take it for granted and do not

More information

2 ways to write the same number: 6,500: standard form 6.5 x 10 3 : scientific notation

2 ways to write the same number: 6,500: standard form 6.5 x 10 3 : scientific notation greater than or equal to one, and less than 10 positive exponents: numbers greater than 1 negative exponents: numbers less than 1, (> 0) (fractions) 2 ways to write the same number: 6,500: standard form

More information

3. What is the decimal place of the least significant figure (LSF) in the number 0.152? a. tenths place b. hundredths place c.

3. What is the decimal place of the least significant figure (LSF) in the number 0.152? a. tenths place b. hundredths place c. Name: Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements =========================================================== Choose the best answer. (30 pts total) Significant Digits,

More information

CHM101 Lab Math Review and Significant Figures Grading Rubric

CHM101 Lab Math Review and Significant Figures Grading Rubric Name CHM101 Lab Math Review and Significant Figures Grading Rubric Criteria Points possible Points earned Part A (0.25 each) 3.5 Part B (0.25 each) 2.5 Part C (0.25 each) 1.5 Part D (Q5 0.25 each, Q6 &

More information

The Grammar and Etiquette of Scientific Math By T. Webb HHS

The Grammar and Etiquette of Scientific Math By T. Webb HHS The Grammar and Etiquette of Scientific Math By T. Webb HHS You can be a mathematician without a lot of science, however, you cannot be a scientist without math Part 1 - Terminology in Basic Data Analysis

More information

LESSON 4-5 THE LAW OF COMMUTATIVITY

LESSON 4-5 THE LAW OF COMMUTATIVITY LESSON 4-5 THE LAW OF COMMUTATIVITY Axioms [AXE ee ums] are things we assume to be true because they seem obvious but we cannot prove them. Say with me: axiom. A. For example, if three plus four is seven,

More information

Essentials of Intermediate Algebra

Essentials of Intermediate Algebra Essentials of Intermediate Algebra BY Tom K. Kim, Ph.D. Peninsula College, WA Randy Anderson, M.S. Peninsula College, WA 9/24/2012 Contents 1 Review 1 2 Rules of Exponents 2 2.1 Multiplying Two Exponentials

More information

University of South Carolina. Stephen L Morgan. Tutorial on the Use of Significant Figures

University of South Carolina. Stephen L Morgan. Tutorial on the Use of Significant Figures University of South Carolina Stephen L Morgan Tutorial on the Use of Significant Figures All measurements are approximations--no measuring device can give perfect measurements without experimental uncertainty.

More information

Polynomials; Add/Subtract

Polynomials; Add/Subtract Chapter 7 Polynomials Polynomials; Add/Subtract Polynomials sounds tough enough. But, if you look at it close enough you ll notice that students have worked with polynomial expressions such as 6x 2 + 5x

More information

Section 4.7 Scientific Notation

Section 4.7 Scientific Notation Section 4.7 Scientific Notation INTRODUCTION Scientific notation means what it says: it is the notation used in many areas of science. It is used so that scientist and mathematicians can work relatively

More information

PHYSICS 30S/40S - GUIDE TO MEASUREMENT ERROR AND SIGNIFICANT FIGURES

PHYSICS 30S/40S - GUIDE TO MEASUREMENT ERROR AND SIGNIFICANT FIGURES PHYSICS 30S/40S - GUIDE TO MEASUREMENT ERROR AND SIGNIFICANT FIGURES ACCURACY AND PRECISION An important rule in science is that there is always some degree of uncertainty in measurement. The last digit

More information

1 Measurement Uncertainties

1 Measurement Uncertainties 1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.

More information

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010 Section 1.1: The Real Number System Definition of set and subset A set is a collection of objects and its objects are called members. If all the members of a set A are also members of a set B, then A is

More information

Section 1.1: Patterns in Division

Section 1.1: Patterns in Division Section 1.1: Patterns in Division Dividing by 2 All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8. Dividing by 4 1. Are the last two digits in your number divisible by 4? 2.

More information

Math 016 Lessons Wimayra LUY

Math 016 Lessons Wimayra LUY Math 016 Lessons Wimayra LUY wluy@ccp.edu MATH 016 Lessons LESSON 1 Natural Numbers The set of natural numbers is given by N = {0, 1, 2, 3, 4...}. Natural numbers are used for two main reasons: 1. counting,

More information

Units and Dimensionality

Units and Dimensionality Chapter 1 Units and Dimensionality If somebody asked me how tall I am, I might respond 1.78. But what do I mean by that? 1.78 feet? 1.78 miles? In fact, my height is 1.78 meters. Most physical measurements

More information

CHM Accuracy, Precision, and Significant Figures (r14) C. Taylor 1/10

CHM Accuracy, Precision, and Significant Figures (r14) C. Taylor 1/10 CHM 110 - Accuracy, Precision, and Significant Figures (r14) - 2014 C. Taylor 1/10 Introduction Observations are vitally important to all of science. Some observations are qualitative in nature - such

More information

Measurements and Data Analysis

Measurements and Data Analysis Measurements and Data Analysis 1 Introduction The central point in experimental physical science is the measurement of physical quantities. Experience has shown that all measurements, no matter how carefully

More information

CHEM Chapter 1

CHEM Chapter 1 CHEM 1110 Chapter 1 Chapter 1 OVERVIEW What s science? What s chemistry? Science and numbers Measurements Unit conversion States of matter Density & specific gravity Describing energy Heat and its transfer

More information

CHAPTER 1. REVIEW: NUMBERS

CHAPTER 1. REVIEW: NUMBERS CHAPTER. REVIEW: NUMBERS Yes, mathematics deals with numbers. But doing math is not number crunching! Rather, it is a very complicated psychological process of learning and inventing. Just like listing

More information

ABE Math Review Package

ABE Math Review Package P a g e ABE Math Review Package This material is intended as a review of skills you once learned and wish to review before your assessment. Before studying Algebra, you should be familiar with all of the

More information

Northwest High School s Algebra 1

Northwest High School s Algebra 1 Northwest High School s Algebra 1 Summer Review Packet 2015 DUE THE FIRST DAY OF SCHOOL Student Name This packet has been designed to help you review various mathematical topics that will be necessary

More information

Appendix B: Skills Handbook

Appendix B: Skills Handbook Appendix B: Skills Handbook Effective communication is an important part of science. To avoid confusion when measuring and doing mathematical calculations, there are accepted conventions and practices

More information

NOTES: Chapter 11. Radicals & Radical Equations. Algebra 1B COLYER Fall Student Name:

NOTES: Chapter 11. Radicals & Radical Equations. Algebra 1B COLYER Fall Student Name: NOTES: Chapter 11 Radicals & Radical Equations Algebra 1B COLYER Fall 2016 Student Name: Page 2 Section 3.8 ~ Finding and Estimating Square Roots Radical: A symbol use to represent a. Radicand: The number

More information

Chapter 3 Scientific Measurement

Chapter 3 Scientific Measurement Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems 1 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

More information

3.1 Using and Expressing Measurements > 3.1 Using and Expressing Measurements >

3.1 Using and Expressing Measurements > 3.1 Using and Expressing Measurements > Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems 1 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

More information

Section 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision?

Section 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision? Lesson Starter Look at the specifications for electronic balances. How do the instruments vary in precision? Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise?

More information

Astronomy 102 Math Review

Astronomy 102 Math Review Astronomy 102 Math Review 2003-August-06 Prof. Robert Knop r.knop@vanderbilt.edu) For Astronomy 102, you will not need to do any math beyond the high-school alegbra that is part of the admissions requirements

More information

Introduction to Chemistry

Introduction to Chemistry Introduction to Chemistry A. Unit Conversions 1. In Chemistry 11 and 12, a mathematical method called Unit Conversions will be used extensively. This method uses CONVERSION FACTORS to convert or change

More information

Mostly Review. Phy 123L

Mostly Review. Phy 123L Name: Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements =========================================================== Choose the best answer. (30 pts total) 1. Do the following

More information

Significant Digits What digits are important when recording a measurement?

Significant Digits What digits are important when recording a measurement? Significant Digits What digits are important when recording a measurement? Why? Scientists do a lot of measuring. When scientists use an instrument (ruler, graduated cylinder, spectrophotometer, balance

More information

Experimental Uncertainty (Error) and Data Analysis

Experimental Uncertainty (Error) and Data Analysis Experimental Uncertainty (Error) and Data Analysis Advance Study Assignment Please contact Dr. Reuven at yreuven@mhrd.org if you have any questions Read the Theory part of the experiment (pages 2-14) and

More information

Notes: Measurement and Calculation

Notes: Measurement and Calculation Name Chemistry-PAP Per. I. The Basics of Measurement Notes: Measurement and Calculation A. Measurement Most provide quantitative information, but because they are obtained experimentally, they are inexact.

More information

Making Measurements. On a piece of scrap paper, write down an appropriate reading for the length of the blue rectangle shown below: (then continue )

Making Measurements. On a piece of scrap paper, write down an appropriate reading for the length of the blue rectangle shown below: (then continue ) On a piece of scrap paper, write down an appropriate reading for the length of the blue rectangle shown below: (then continue ) 0 1 2 3 4 5 cm If the measurement you made was 3.7 cm (or 3.6 cm or 3.8 cm),

More information

Massachusetts Tests for Educator Licensure (MTEL )

Massachusetts Tests for Educator Licensure (MTEL ) Massachusetts Tests for Educator Licensure (MTEL ) BOOKLET 2 Mathematics Subtest Copyright 2010 Pearson Education, Inc. or its affiliate(s). All rights reserved. Evaluation Systems, Pearson, P.O. Box 226,

More information

Physics 10 Scientific Measurement Workbook Mr. Proctor

Physics 10 Scientific Measurement Workbook Mr. Proctor Physics 10 Scientific Measurement Workbook Mr. Proctor Name: MEASUREMENT OF MATTER - Science 10 textbook reference pages 344-351 The Seven Fundamental Measurements (with units) in Physics are: meter (m)

More information

Northwest High School s Algebra 1

Northwest High School s Algebra 1 Northwest High School s Algebra 1 Summer Review Packet 2011 DUE WEDNESDAY, SEPTEMBER 2, 2011 Student Name This packet has been designed to help you review various mathematical topics that will be necessary

More information

Chapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers

Chapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,

More information

Appendix F. Treatment of Numerical Data. I. Recording Data F-1

Appendix F. Treatment of Numerical Data. I. Recording Data F-1 Treatment of umerical Data I. Recording Data When numerical data are recorded, three kinds of information must be conveyed: the magnitude of the number, how well the number is known, and the units used

More information

Scientific Notation Review

Scientific Notation Review Summer Packet AP Physics B Use the internet for additional reference on the following problems. Complete all problems!! You must bring this on the first day of school it will count as your first exam!!

More information

Accuracy and Precision of Laboratory Glassware: Determining the Density of Water

Accuracy and Precision of Laboratory Glassware: Determining the Density of Water Accuracy and Precision of Laboratory Glassware: Determining the Density of Water During the semester in the general chemistry lab, you will come into contact with various pieces of laboratory glassware.

More information

EXPERIMENTAL UNCERTAINTY

EXPERIMENTAL UNCERTAINTY 3 EXPERIMENTAL UNCERTAINTY I am no matchmaker, as you well know, said Lady Russell, being much too aware of the uncertainty of all human events and calculations. --- Persuasion 3.1 UNCERTAINTY AS A 95%

More information

A.0 SF s-uncertainty-accuracy-precision

A.0 SF s-uncertainty-accuracy-precision A.0 SF s-uncertainty-accuracy-precision Objectives: Determine the #SF s in a measurement Round a calculated answer to the correct #SF s Round a calculated answer to the correct decimal place Calculate

More information

LESSON ASSIGNMENT. After completing this lesson, you should be able to:

LESSON ASSIGNMENT. After completing this lesson, you should be able to: LESSON ASSIGNMENT LESSON 1 General Mathematics Review. TEXT ASSIGNMENT Paragraphs 1-1 through 1-49. LESSON OBJECTIVES After completing this lesson, you should be able to: 1-1. Identify and apply the properties

More information

Patterning the Powers of 10 Learning Strategies

Patterning the Powers of 10 Learning Strategies What should students be able to do? Patterning the Powers of 0 Learning Strategies Students should be able to correctly order base 0 exponents using patterns and understand the meaning of a positive and

More information

The periodic table currently lists 116 different atoms. New atoms are being discovered.

The periodic table currently lists 116 different atoms. New atoms are being discovered. CHEM100 Week 1 Notes Page 1 of 11 Chemistry is the study of matter. Matter is made up of atoms. The periodic table currently lists 116 different atoms. New atoms are being discovered. Atoms consist of

More information

Northwest High School s Geometry

Northwest High School s Geometry Northwest High School s Geometry Summer Math Packet (For 2013-2014) DUE THE FIRST DAY OF SCHOOL Student Name: - 1 - This packet has been designed to help you review various mathematical topics that will

More information

Uncertainty: A Reading Guide and Self-Paced Tutorial

Uncertainty: A Reading Guide and Self-Paced Tutorial Uncertainty: A Reading Guide and Self-Paced Tutorial First, read the description of uncertainty at the Experimental Uncertainty Review link on the Physics 108 web page, up to and including Rule 6, making

More information

A Justification for Sig Digs

A Justification for Sig Digs A Justification for Sig Digs Measurements are not perfect. They always include some degree of uncertainty because no measuring device is perfect. Each is limited in its precision. Note that we are not

More information

Chapter 1. Foundations of GMAT Math. Arithmetic

Chapter 1. Foundations of GMAT Math. Arithmetic Chapter of Foundations of GMAT Math In This Chapter Quick-Start Definitions Basic Numbers Greater Than and Less Than Adding and Subtracting Positives and Negatives Multiplying and Dividing Distributing

More information

Chemistry Chapter 2 Data Analysis

Chemistry Chapter 2 Data Analysis Chemistry Chapter 2 Data Analysis I. Units of Measurement 2.1 (pages 25-30) A. The metric system (SI units) Why the metric system? B. Base Units of the SI System Based on an object or event of the of other

More information

Maths skills: resource 1

Maths skills: resource 1 Maths skills: resource 1 Scientific notation Going up: powers of ten for large numbers It is estimated that the total volume of water stored on the Earth is 1,460,000,000 km 3. When dealing with large

More information

Introduction to 1118 Labs

Introduction to 1118 Labs Name: Partner(s): 1118 section: Desk # Date: Introduction to 1118 Labs Introductory materials are at: www.langaraphysics.com/lab.html. You may find following 3 links useful for this lab: Measurements:

More information

Chemistry 320 Approx. Time: 45 min

Chemistry 320 Approx. Time: 45 min Chemistry 320 Approx. Time: 45 min Name: 02.02.02.a1 Most Important Idea: Date: Purpose The purpose of this activity is to be able to write numbers in both standard and scientific notation, and to be able

More information

NUMBER. Here are the first 20 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

NUMBER. Here are the first 20 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71. NUMBER Types of Number Prime Numbers A prime number is a number which can only be divided by 1 or itself. The smallest prime number is 2. 2 can only be divided by 2 or 1. Here are the first 20 prime numbers:

More information

Numbers and Uncertainty

Numbers and Uncertainty Significant Figures Numbers and Uncertainty Numbers express uncertainty. Exact numbers contain no uncertainty. They are obtained by counting objects (integers) or are defined, as in some conversion factors

More information

Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding)

Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding) Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding) Goals: To be able to convert quantities from one unit to another. To be able to express measurements and answers to the correct

More information

Physics 2020 Laboratory Manual

Physics 2020 Laboratory Manual Physics 00 Laboratory Manual Department of Physics University of Colorado at Boulder Spring, 000 This manual is available for FREE online at: http://www.colorado.edu/physics/phys00/ This manual supercedes

More information

EQ: How do I convert between standard form and scientific notation?

EQ: How do I convert between standard form and scientific notation? EQ: How do I convert between standard form and scientific notation? HW: Practice Sheet Bellwork: Simplify each expression 1. (5x 3 ) 4 2. 5(x 3 ) 4 3. 5(x 3 ) 4 20x 8 Simplify and leave in standard form

More information

Finding Prime Factors

Finding Prime Factors Section 3.2 PRE-ACTIVITY PREPARATION Finding Prime Factors Note: While this section on fi nding prime factors does not include fraction notation, it does address an intermediate and necessary concept to

More information

Percent Problems. Percent problems can be solved using proportions. Use the following formula when solving percent problems with a proportion.

Percent Problems. Percent problems can be solved using proportions. Use the following formula when solving percent problems with a proportion. Percent Problems Percent problems can be solved using proportions. Use the following formula when solving percent problems with a proportion. The whole is the number after the word of. The percent is the

More information

Why the fuss about measurements and precision?

Why the fuss about measurements and precision? Introduction In this tutorial you will learn the definitions, rules and techniques needed to record measurements in the laboratory to the proper precision (significant figures). You should also develop

More information

Chemistry Basic Science Concepts. Observations: are recorded using the senses. Examples: the paper is white; the air is cold; the drink is sweet.

Chemistry Basic Science Concepts. Observations: are recorded using the senses. Examples: the paper is white; the air is cold; the drink is sweet. Note Packet # 1 1 Chemistry: the study of matter. Chemistry Basic Science Concepts Matter: anything that has mass and occupies space. Observations: are recorded using the senses. Examples: the paper is

More information

Chapter 2 Math Skills

Chapter 2 Math Skills Chapter 2 Math Skills 2.1 Measurements Measurement number with a unit Units are very important o A student wouldn t ask a teacher Could you please hand me 6? The student would instead ask, Could you please

More information

Part 01 - Notes: Identifying Significant Figures

Part 01 - Notes: Identifying Significant Figures Part 01 - Notes: Identifying Significant Figures Objectives: Identify the number of significant figures in a measurement. Compare relative uncertainties of different measurements. Relate measurement precision

More information

Appendix A. Review of Basic Mathematical Operations. 22Introduction

Appendix A. Review of Basic Mathematical Operations. 22Introduction Appendix A Review of Basic Mathematical Operations I never did very well in math I could never seem to persuade the teacher that I hadn t meant my answers literally. Introduction Calvin Trillin Many of

More information

Summer Review. For Students Entering. Algebra 2 & Analysis

Summer Review. For Students Entering. Algebra 2 & Analysis Lawrence High School Math Department Summer Review For Students Entering Algebra 2 & Analysis Fraction Rules: Operation Explanation Example Multiply Fractions Multiply both numerators and denominators

More information

Prerequisites. Introduction CHAPTER OUTLINE

Prerequisites. Introduction CHAPTER OUTLINE Prerequisites 1 Figure 1 Credit: Andreas Kambanls CHAPTER OUTLINE 1.1 Real Numbers: Algebra Essentials 1.2 Exponents and Scientific Notation 1.3 Radicals and Rational Expressions 1.4 Polynomials 1.5 Factoring

More information

Chemistry 1. Worksheet 3. Significant Figures in Calculations. 1 MathTutorDVD.com

Chemistry 1. Worksheet 3. Significant Figures in Calculations. 1 MathTutorDVD.com Chemistry 1 Worksheet 3 Significant Figures in Calculations 1 Report all answers on this worksheet with the correct number of significant figures. 1) How many significant figures does each of the following

More information

Experiment 1 Simple Measurements and Error Estimation

Experiment 1 Simple Measurements and Error Estimation Experiment 1 Simple Measurements and Error Estimation Reading and problems (1 point for each problem): Read Taylor sections 3.6-3.10 Do problems 3.18, 3.22, 3.23, 3.28 Experiment 1 Goals 1. To perform

More information

Measurements. October 06, 2014

Measurements. October 06, 2014 Measurements Measurements Measurements are quantitative observations. What are some kinds of quantitative observations you might make? Temperature Volume Length Mass Student A and Student B measured the

More information

Rounding. In mathematics rounding off is writing an answer to a given degree of accuracy.

Rounding. In mathematics rounding off is writing an answer to a given degree of accuracy. Rounding In mathematics rounding off is writing an answer to a given degree of accuracy. Let's round off 314 to the nearest hundred. You know that 314 is closer to 300 than 400, so when we rounded off

More information

PHY 123 Lab 1 - Error and Uncertainty and the Simple Pendulum

PHY 123 Lab 1 - Error and Uncertainty and the Simple Pendulum To print higher-resolution math symbols, click the Hi-Res Fonts for Printing button on the jsmath control panel. PHY 13 Lab 1 - Error and Uncertainty and the Simple Pendulum Important: You need to print

More information

What Fun! It's Practice with Scientific Notation!

What Fun! It's Practice with Scientific Notation! What Fun! It's Practice with Scientific Notation! Review of Scientific Notation Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000

More information

Intermediate Math Circles February 14, 2018 Contest Prep: Number Theory

Intermediate Math Circles February 14, 2018 Contest Prep: Number Theory Intermediate Math Circles February 14, 2018 Contest Prep: Number Theory Part 1: Prime Factorization A prime number is an integer greater than 1 whose only positive divisors are 1 and itself. An integer

More information