A Justification for Sig Digs
|
|
|
- Clarence Nash
- 5 years ago
- Views:
Transcription
1 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 talking about human errors here.
2 Precision We indicate the precision to which we measured our quantity in how we write our measurement. For example, which measurement is more precise? 15 cm 15.0 cm This one, obviously. Physicists are lazy. They wouldn t bother to write the.0 if they didn t mean it.
3 What we mean When we write 15 cm, we mean that we ve measured the quantity to be closer to 15 cm than to 14 cm or 16 cm BUT When we write 15.0 cm, we mean that we ve measured the quantity to be closer to 15 cm than to 14.9 cm or 15.1 cm.
4 Significance Digits that have been measured are said to be significant. 15 cm This measurement has cm This measurement has 3.
5 The following rules are used to determine if a digit is significant: All non-zero digits are significant e.g N has three significant digits
6 The following rules are used to determine if a digit is significant: All non-zero digits are significant Any zeroes placed after other digits and behind a decimal are significant e.g kg has three significant digits
7 The following rules are used to determine if a digit is significant: All non-zero digits are significant Any zeroes placed after other digits and behind a decimal are significant Any zeroes placed between significant digits are significant e.g m has four significant digits
8 The following rules are used to determine if a digit is significant: All non-zero digits are significant Any zeroes placed after other digits and behind a decimal are significant Any zeroes placed between significant digits are significant All other zeroes are not significant e.g. both 100 cm and kg each have only one significant digit
9 How can you say those digits are not significant? Both 100 cm and kg each have only one sig dig? The zeros here are placeholders they re just there to show in which place the non-zeros belong. If the measurements are rewritten 1 m and 4 g, it becomes apparent that there s only one sig dig. But what if you measured 100 cm exactly?
10 Making Zeros Significant But what if you measured 100 cm exactly? You can show that a zero is significant by either: underscoring or overscoring the zero: 100 cm (if the measurement is in a table) rewriting the measurement in scientific notation: 1.00 x 10 2 cm
11 Making Zeros Significant And yes, if you measure a zero, you must write it. Your lab tables should not look like this: Time (s) Distance (cm)
12 Making Zeros Significant They should look like this: Time (s) Distance (cm)
13 No ½ measurements Your tables also should not look like this: Time (s) Distance (cm)
14 No ½ measurements If you can clearly measure.5 in one case, surely you could measure to the tenths place in the other cases too? We don t use.5 to substitute for about ½ :.5 means closer to.5 than to.4 or.6. Be exact. Time (s) Distance (cm)
15 How many significant digits are there in each of the following? 25 W 60 km/h 305 K 3.6 kg 5.0 mt 0.1 N cal
16 How many significant digits are there in each of the following? 25 W 60 km/h 305 K 3.6 kg 5.0 mt 0.1 N cal 2 s.d. 1 s.d. 3 s.d. 2 s.d. 2 s.d. 1 s.d. 4 s.d.
17 How many significant digits are there in each of the following? 1.10 A h MHz 2100 kj W kg km
18 How many significant digits are there in each of the following? 1.10 A h MHz 2100 kj W kg km 3 s.d. 2 s.d. 4 s.d. 2 s.d. 4 s.d. 4 s.d. 5 s.d.
19 Round each measurement to the required significant digits: 4080 J to 1 s.d J to 2 s.d kg to 1 s.d kg to 2 s.d V to 1 s.d V to 2 s.d.
20 Round each measurement to the required significant digits: 4080 J to 1 s.d J to 2 s.d kg to 1 s.d kg to 2 s.d V to 1 s.d V to 2 s.d J 4100 J 3 kg 2.7 kg 1 V 0.99 V
21 Write each of the following in scientific notation cal 1200 N J km s 20.5 khz
22 Write each of the following in scientific notation cal 1200 N J km s 20.5 khz cal N J km s khz
23 The Final Answer When a measurement is used in a calculation, the final answer must take into consideration the uncertainty in the original measurements. Why? You don t want to suggest that you know something to a greater precision than you actually measured. For example, 4 m/3 s = m/s???
24 The Final Answer When a measurement is used in a calculation, the final answer must take into consideration the uncertainty in the original measurements. Why? You don t want to suggest that you know something to a greater precision than you actually measured. For example, 4 m/3 s = 1 m/s.
25 The Final Answer When a measurement is used in a calculation, the final answer must take into consideration the uncertainty in the original measurements. Note: Exact numbers used in calculations (e.g. a factor such as ½ in the equation K=½mv 2 ) are not measurements and do not have any uncertainty.
26 Addition and Subtraction When adding or subtracting measurements, the final answer should be rounded off to the least number of decimals in the original measurements. e.g cm (3 decimal places) cm (2 decimal places) 5.13 cm (2 decimal places)
27 Practice 7 m + 7 m = 7 m m = 7.0 m m =
28 Practice 7 m + 7 m = 14 m 7 m m = 14 m 7.0 m m = 14.0 m
29 Multiplication and Division When multiplying or dividing measurements, the final answer should be rounded off to the same number of sig digs as are in the measurement with the least number of sig digs. e.g cm (4 sig digs) x 0.01 cm (1 sig dig) 0.05 cm 2 (1 sig dig)
30 Practice 7 m x 7 m = 7 m x 7.0 m = 7.0 m x 7.0 m =
31 Practice 7 m x 7 m = 50 m 2 (Yes, your math teacher would not approve.) 7 m x 7.0 m = 7.0 m x 7.0 m =
32 Practice 7 m x 7 m = 50 m 2 7 m x 7.0 m = 50 m m x 7.0 m = 49 m 2
33 More Practice ½(5.0 kg)(20 m/s) 2 = ½(5.0 kg)(20.0 m/s) 2 = kg 120N / m kg N / m
34 More Practice ½(5.0 kg)(20 m/s) 2 = 1000 J ½(5.0 kg)(20.0 m/s) 2 = 1.0 x 10 3 J kg 0. 41s 120N / m kg s N / m
35 A Warning When solving multi-step problems, round-off error can occur if a rounded-off answer from one step is used in a later step. Record or store in your calculator all calculated digits for use in later steps. SERIOUSLY!!!! DON T ROUND TOO SOON
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
Base unit-a defined unit of measurement based on an object or event in the physical world. Length
Base unit-a defined unit of measurement based on an object or event in the physical world Five base units: Temperature Mass Length Time Energy Derived unit-a unit of measurement defined by a combination
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
Measurement. New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 -
Measurement Unit Description In this unit we will focus on the mathematical tools we use in science, especially chemistry the metric system and moles. We will also talk about how to gauge the accuracy
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
(Significant Digits are in BOLD type and the non-significant digits are underlined)
Name Per. Date Significant Digits Worksheet Significant digits (or significant figures) are used to represent the accuracy of a measurement. In a measurement the significant digits represent all the reliable
PHY 101L - Experiments in Mechanics
PHY 101L - Experiments in Mechanics introduction to error analysis What is Error? In everyday usage, the word error usually refers to a mistake of some kind. However, within the laboratory, error takes
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
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
NAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
Rules for Determining Significant Digits
Significant Figures Name: Per: aka: Significant Digits Certain Digits: Numbers you are sure of. Uncertain Digits: Last number is an estimate. Certain Digits & Uncertain digits Measurement made with instruments
Do Now: Use the ruler below to answer the following questions
Chemistry Ms. Ye Name Date Block Do Now: Use the ruler below to answer the following questions 1. What is each tick mark worth on the ruler? 2. When measuring, to which decimal place should you estimate
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
The Rules of the Game
The Rules of the Game Over hundreds of years ago, physicists and other scientists developed a traditional way of expressing their observations. International System of Units (SI) metric system. The amount
Physics 20. Introduction & Review. Real tough physics equations. Real smart physics guy
Physics 20 Introduction & Review Real tough physics equations Real smart physics guy Is Physics Hard? People find physics difficult because it requires a detail-oriented, organized thought process. Success,
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
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
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
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
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
1. Volume=amount of an object takes up Ways we can measure volume:
Chemistry Ms. Ye Name Date Block A physical property is something that can be measured or observed without changing the chemical composition of the substance. Mass, volume, and density or examples of physical
Physics 12 Rules for Significant Digits and Rounding
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
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
Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific
Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific notation in calculations. Significant figures - consist of
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
Uncertainty in Measurements
Uncertainty in Measurements! Two kinds of numbers " Exact! counted values " 2 dogs " 26 letters " 3 brothers! defined numbers " 12 inches per foot " 1000 g per kilogram " 2.54 cm per inch Metric Practice!
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.
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.
Allows us to work with very large or small numbers more easily. All numbers are a product of 10.
Unit 1: Measurements Scientific Notation : Allows us to work with very large or small numbers more easily. All numbers are a product of 10. M x 10n M= signif. digit [ 1 < M < 10 ] n = an integer move the
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
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 &
Unit 2. Scientific Measurement
Unit 2 Scientific Measurement Qualitative vs quantitative Qualitative measurementsgive results in a descriptive, non-numerical form Ex. Observations taken in the demo lab Quantitative measurementsgive
Chapter 4: Radicals and Complex Numbers
Section 4.1: A Review of the Properties of Exponents #1-42: Simplify the expression. 1) x 2 x 3 2) z 4 z 2 3) a 3 a 4) b 2 b 5) 2 3 2 2 6) 3 2 3 7) x 2 x 3 x 8) y 4 y 2 y 9) 10) 11) 12) 13) 14) 15) 16)
Prepared by Sa diyya Hendrickson. Package Summary
Introduction Prepared by Sa diyya Hendrickson Name: Date: Package Summary Understanding Variables Translations The Distributive Property Expanding Expressions Collecting Like Terms Solving Linear Equations
A. Incorrect. Solve for a variable on the bottom by first moving it to the top. D. Incorrect. This answer has too many significant figures.
MCAT Physics - Problem Drill 03: Math for Physics Question No. 1 of 10 1. Solve the following equation for time, with the correct number of significant figures: Question #01 m 15.0 m 2.5 = s time (A) 0.17
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?
Uncertainties in Measurement
Uncertainties in Measurement Laboratory investigations involve taking measurements of physical quantities. All measurements will involve some degree of experimental uncertainty. QUESTIONS 1. How does one
welcome to physics! 1.1 Mathematics and Physics
welcome to physics! 1.1 Mathematics and Physics What is Physics? - study of energy, matter and how they are related - motion, energy of sound waves, electric circuits, etc Mathematics in Physics - use
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
Exponents are a short-hand notation for writing very large or very. small numbers. The exponent gives the number of times that a number
UNIT 3 EXPONENTS Math 11 Unit 3 Introduction p. 1 of 1 A. Algebraic Skills Unit 3 Exponents Introduction Exponents are a short-hand notation for writing ver large or ver small numbers. The exponent gives
Tools of Chemistry. Measurement Scientific Method Lab Safety & Apparatus
Tools of Chemistry Measurement Scientific Method Lab Safety & Apparatus Scientific Notation Scientific Notation a number described as a power of 10 (used for very large or small numbers) 1000 = 1 X 10
Notes: Unit 1: Math and Measurement
Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)
Notes: Unit 1: Math and Measurement
Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)
Metric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER?
UNITS & MEASUREMENT WHY DO UNITS AND MEASUREMENT MATTER? Chemistry In Action On 9/3/99, $15,000,000 Mars Climate Orbiter entered Mar s atmosphere 100 km (6 miles) lower than planned and was destroyed by
How long is the arrow?
1.2 Measurements Measuring We have all measured things before, but how would you define it? Measurement: comparing an unknown quantity to a standard unit (known quantity) How long is the arrow? Any measurement
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
Math-2. Lesson 1-2 Solving Single-Unknown Linear Equations
Math-2 Lesson 1-2 Solving Single-Unknown Linear Equations Linear Equation: an equation where all of the letters (either variables or unknown values) have NO EXPONENTS. 4x 2 = 6 2x + 3y = 6 Previous Vocabulary
Scientific Measurement
Scientific Measurement A quantity is anything having a measurable size or amount For Example: 5 But 5 what? A unit assigns value to a measured quantity For Example: 5 ft, 5 gal, 5 sec, 5 m, 5 g. Base Units
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
Chapter 3 Math Toolkit
Chapter 3 Math Toolkit Problems - any Subtitle: Error, where it comes from, how you represent it, and how it propagates into your calculations. Before we can start talking chemistry we must first make
Accuracy: An accurate measurement is a measurement.. It. Is the closeness between the result of a measurement and a value of the measured.
Chemical Analysis can be of two types: Chapter 11- Measurement and Data Processing: - : Substances are classified on the basis of their or properties, such as - : The amount of the sample determined in
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
Physics Mechanics. Lecture 1 Physics and the Laws of Nature
Physics 170 - Mechanics Lecture 1 Physics and the Laws of Nature 1 Physics: the study of the fundamental laws of nature These laws can be expressed as mathematical equations. (e.g. F = ma, E=mc 2 ) Most
COLLEGE PHYSICS. Chapter 1 INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS. Lesson 2
COLLEGE PHYSICS Chapter 1 INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS Lesson 2 Video Narrated by Jason Harlow, Physics Department, University of Toronto MEASUREMENTS Here are two different kinds of
Measurement and Uncertainty. To determine the uncertainty associated with various measuring devices.
Chemistry 11 Lab #1 Measurement and Uncertainty Name: Date: Block: Purpose To determine the uncertainty associated with various measuring devices. Procedure 1) Balances Weigh the same cylinder with five
Introduction to Measurement Physics 114 Eyres
1 Introduction to Measurement Physics 114 Eyres 6/5/2016 Module 1: Measurement 1 2 Significant Figures Count all non-zero digits Count zeros between non-zero digits Count zeros after the decimal if also
Measurement Error PHYS Introduction
PHYS 1301 Measurement Error Introduction We have confidence that a particular physics theory is telling us something interesting about the physical universe because we are able to test quantitatively its
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
Chemistry: The Study of Change Chang & Goldsby 12 th edition
Chemistry: The Study of Change Chang & Goldsby 12 th edition modified by Dr. Hahn Chapter 1 Example 1.4 Determine the number of significant figures in the following measurements: (a)478 cm (b)6.01 g end
PHYSICS!!! (SPH3U) Key concepts: physics scientific inquiry observation qualitative quantitative metric precision accuracy
PHYSICS!!! (SPH3U) physics scientific inquiry observation qualitative quantitative metric precision accuracy PHYSICS!!! (SPH3U) physics scientific inquiry observation qualitative quantitative metric precision
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
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.
Significant figures. We estimated the last digit, It's uncertain
21 Significant figures SIGNIFICANT FIGURES are a way to indicate the amount of uncertainty in a measurement. The significant figures in a measurement are all of the CERTAIN DIGITS plus one and only one
161 Sp18 T1 grades (out of 40, max 100)
Grades for test Graded out of 40 (scores over 00% not possible) o Three perfect scores based on this grading scale!!! o Avg = 57 o Stdev = 3 Scores below 40% are in trouble. Scores 40-60% are on the bubble
How do physicists study problems?
What is Physics? The branch of science that studies the physical world (from atoms to the universe); The study of the nature of matter and energy and how they are related; The ability to understand or
Today is Thursday, February 8 th, 2018
In This Lesson: Measurement and Significant Figures (Lesson 3 of 6) Today is Thursday, February 8 th, 2018 Stuff You Need: Calculator Pre-Class: Get your calculators and get ready. Something else to do:
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
This term refers to the physical quantity that is the result of the measurement activity.
Metrology is the science of measurement and involves what types of measurements are possible, standards, how to properly represent a number and how to represent the uncertainty in measurement. In 1993
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.
Work Session 2: Introduction to Measurements, Conversions, and Significant Figures
Work Session 2: Introduction to Measurements, Conversions, and Significant Figures Measurements are made using tools. The tool can be as simple as a ruler or as complex as the Hubble Space Telescope. It
SCIENTIFIC MEASUREMENT C H A P T E R 3
SCIENTIFIC MEASUREMENT C H A P T E R 3 WHAT IS MEASUREMENT? Comparing one object to a standard In science, we use SI Units meters, o C, grams NOT o F, pounds, ounces etc. TWO TYPES OF MEASUREMENTS 1.
Chapter 2. Measurements and Calculations
Chapter 2 Measurements and Calculations Section 2.1 Scientific Notation Measurement Quantitative observation. Has 2 parts number and unit. Number tells comparison. Unit tells scale. If something HAS a
2 Foundations of physics Calculation sheet. OCR Physics A. Determining uncertainty. Specification references. Learning outcomes
Determining uncertainty Specification references 2.2.1 c) M0.3 Use ratios, fractions, and percentages M1.5 Identify uncertainties in measurements and use simple techniques to determine uncertainty when
Chapter 1. Chemistry and Measurements
Chapter 1 Chemistry and Measurements Section 1-1 Chemistry: the study of matter and the changes it undergoes. macroscopic: relating to large-scale analysis, visible to the naked eye microscopic: not visible
Investigation 1: How Thick is Aluminum Foil?
Investigation 1: How Thick is Aluminum Foil? Purpose: 1. To determine the thickness of one sheet of aluminum foil in centimeters. 2. To determine the thickness of aluminum foil in terms of atoms of aluminum.
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.
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
Alg. 1 Radical Notes
Alg. 1 Radical Notes Evaluating Square Roots and Cube Roots (Day 1) Objective: SWBAT find the square root and cube roots of monomials Perfect Squares: Perfect Cubes: 1 =11 1 = 11 =1111 11 1 =111 1 1 =
Physics. Nov Title: Nov 3 8:52 AM (1 of 45)
Physics Nov 3 2008 Title: Nov 3 8:52 AM (1 of 45) Physics Nov 3 2008 Physics is the branch of science that studies matter and energy, how they are related and how they interact. Physics covers everything
Arthur & Polly Mays Conservatory Of The Arts
Arthur & Polly Mays Conservatory Of The Arts Dear Honors Chemistry Student, This packet is prepared to provide entering students of Honors Chemistry with practice to be familiar with the following skills
TOPIC 3: READING AND REPORTING NUMERICAL DATA
Page 1 TOPIC 3: READING AND REPORTING NUMERICAL DATA NUMERICAL DATA 3.1: Significant Digits; Honest Reporting of Measured Values Why report uncertainty? That is how you tell the reader how confident to
Unit 2: Data Analysis. Chapter 2
Unit 2: Data Analysis Chapter 2 I.Units of Measurement A.SI System (Système International d'unités): modern version of the metric system. 1. The USA is the only country in the world which has not fully
Principles and Problems. Chapter 1: A Physics Toolkit
PHYSICS Principles and Problems Chapter 1: A Physics Toolkit CHAPTER 1 A Physics Toolkit BIG IDEA Physicists use scientific methods to investigate energy and matter. CHAPTER 1 Table Of Contents Section
Scientific Notation. Chemistry Honors
Scientific Notation Chemistry Honors Used to easily write very large or very small numbers: 1 mole of a substance consists of 602,000,000,000,000,000,000,000 particles (we ll come back to this in Chapter
Graphing Radicals Business 7
Graphing Radicals Business 7 Radical functions have the form: The most frequently used radical is the square root; since it is the most frequently used we assume the number 2 is used and the square root
MEASUREMENT AND PROBLEM SOLVING. Chapter 3 & 4
MEASUREMENT AND PROBLEM SOLVING Chapter 3 & 4 Importance of Measurements 1. Fundamental to all sciences 2. In chemistry you use the International System of Measurements (SI units). Qualitative vs. Quantitative
Eby, MATH 0310 Spring 2017 Page 53. Parentheses are IMPORTANT!! Exponents only change what they! So if a is not inside parentheses, then it
Eby, MATH 010 Spring 017 Page 5 5.1 Eponents Parentheses are IMPORTANT!! Eponents only change what they! So if a is not inside parentheses, then it get raised to the power! Eample 1 4 b) 4 c) 4 ( ) d)
Name: Chapter 2: Analyzing Data Note Taking Guide This worksheet is meant to help us learn some of the basic terms and concepts of chemistry.
Chemistry Name: Section ANALYZE DATA KEY Date: Chapter 2: Analyzing Data Note Taking Guide This worksheet is meant to help us learn some of the basic terms and concepts of chemistry. Most, but not all,
MEASUREMENT IN THE LABORATORY
1 MEASUREMENT IN THE LABORATORY INTRODUCTION Today's experiment will introduce you to some simple but important types of measurements commonly used by the chemist. You will measure lengths of objects,
You separate binary numbers into columns in a similar fashion. 2 5 = 32
RSA Encryption 2 At the end of Part I of this article, we stated that RSA encryption works because it s impractical to factor n, which determines P 1 and P 2, which determines our private key, d, which
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
Working with Square Roots. Return to Table of Contents
Working with Square Roots Return to Table of Contents 36 Square Roots Recall... * Teacher Notes 37 Square Roots All of these numbers can be written with a square. Since the square is the inverse of the
ERROR AND GRAPHICAL ANALYSIS WORKSHEET
Student Names: Course: Section: Instructor: ERROR AND GRAPHICAL ANALYSIS WORKSHEET Instructions: For each section of this assignment, first read the relevant section in the Yellow Pages of your Lab Manual.
CHAPTER 9 : Motion Physics Intro to MEASUREMENTS
CHAPTER 9 : Motion Physics Intro to MEASUREMENTS SIGNIFICANT FIGURES SCIENTIFIC NOTATION CALCULATIONS ACCURACY AND PRECICION ERRORS REVIEW OF METRIC SYSTEM Significant figures and calculations Significant
Lesson 5: Significant Digits. AKA Significant Figures
Lesson 5: Significant Digits AKA Significant Figures First, take HW out to be checked. Keep it out. In CJ, copy down info from board. Keep CJ open to today s date at the top corner of your desk. On your
MEASUREMENT UNCERTAINTIES
MEASUREMENT UNCERTAINTIES What distinguishes science rom philosophy is that it is grounded in experimental observations. These observations are most striking when they take the orm o a quantitative measurement.
Methods and Tools of Physics
Methods and Tools of Physics Order of Magnitude Estimation: Essential idea: Scientists aim towards designing experiments that can give a true value from their measurements, but due to the limited precision
CHM 130 Measurements, Significant Figures, Derived Quantities, and Unit Conversions
CHM 130 Measurements, Significant Figures, Derived Quantities, and Unit Conversions Objectives 1. Use measuring tools correctly 2. Read and record measurements correctly (significant digits and unit) 3.
POGIL: Sig Figs in Calculations
Name: Date: Period: Chemistry POGIL: Sig Figs in Calculations WHY? Many of the measurements a scientist makes in lab are further analyzed or used to calculate derived units, such as area, speed, and pressure.
Name. Academic Chemistry Measurement and Calculations. Notes. Measurement cincochem.pbworks.com 1
Name Academic Chemistry Measurement and Calculations Notes Measurement cincochem.pbworks.com 1 Academic Chemistry SIGNIFICANT FIGURES Unit 1 Significant figures are the digits in a measurement that you