Scientific Notation. Section 7-1 Part 2

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Scientific Notation. Section 7-1 Part 2"

Transcription

1 Scientific Notation Section 7-1 Part 2

2 Goals Goal To write numbers in scientific notation and standard form. To compare and order numbers using scientific notation.

3 Vocabulary Scientific Notation

4 Powers of 10 The table shows relationships between several powers of 10. Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left. Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.

5 Powers of 10 You can find the product of a number and a power of 10 by moving the decimal point of the number. If the exponent is positive, move the decimal point to the right. If the exponent is negative, move the decimal point to the left. You may need to write zeros to the right or left of the number in order to move the decimal point.

6 Multiply. Example: Multiplying by Powers of 10 A. 14 x Since the exponent is a positive 4, move the decimal point 4 places to the right. 140,000 B. 3.6 x Since the exponent is a negative 5, move the decimal point 5 places to the left

7 Your Turn: Multiply. A. 2.5 x Since the exponent is a positive 5, move the decimal point 5 places to the right. 250,000 B x Since the exponent is a negative 3, move the decimal point 3 places to the left

8 Definition Scientific Notation - is a way to express numbers that are very large or very small. Powers of 10 are used when writing numbers in scientific notation. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10. Example:

9 Scientific Notation The first part is a number that is greater than or equal to 1 and less than 10. The second part is a power of 10.

10 Why Use Scientific Notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

11 Example: Recognizing Scientific Notation Is the number written in scientific notation? Explain No, 53 is not less than Yes No, 0.35 is not greater than or equal to 1 No, 100 is not in power of 10 form

12 Your Turn: Is the number written in scientific notation? Explain Yes No, 12.9 is greater than Yes No, is not greater than or equal to 1

13 Procedure: Writing Numbers in Scientific Notation 1. Place the decimal point so that there is one nonzero digit to the left of the decimal point. 2. Count the number of decimal places the decimal point has moved from the original number. This will be the exponent on the If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

14 Example: Writing Numbers in Scientific Notation Write the number in scientific notation. A Think: The decimal needs to move 3 places to get a number between 1 and x 10-3 Think: The number is less than 1, so the exponent will be negative. So written in scientific notation is 7.09 x 10 3.

15 Example: Writing Numbers in Scientific Notation Write the number in scientific notation. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and x Think: The number is greater than 1, so the exponent will be positive. So 23,000,000,000 written in scientific notation is 2.3 x

16 Your Turn: Write the number in scientific notation. A Think: The decimal needs to move 4 places to get a number between 1 and x 10-4 Think: The number is less than 1, so the exponent will be negative. So written in scientific notation is 8.11 x 10 4.

17 Your Turn: Write the number in scientific notation. B. 480,000,000 Think: The decimal needs to move 8 places to get a number between 1 and x 10 8 Think: The number is greater than 1, so the exponent will be positive. So 480,000,000 written in scientific notation is 4.8 x 10 8.

18 Reading Math Standard form refers to the usual way that numbers are written not in scientific notation.

19 Procedure: Writing Numbers in Standard Form 1. Simply move the decimal point to the right for positive exponent Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

20 Example: Writing a Number in Standard Form Write the number in standard form. A x x Think: Move the decimal right 5 places. 135,000

21 Example: Writing a Number in Standard Form Write the number in standard form. B. 2.7 x x Think: Move the decimal left 3 places

22 A x x 10 9 Your Turn: Write the number in standard form Think: Move the decimal right 9 places. 2,870,000,000

23 Your Turn: Write the number in standard form. B. 1.9 x x Think: Move the decimal left 5 places

24 Example: Comparing Numbers in Scientific Notation A certain cell has a diameter of approximately 4.11 x 10-5 meters. A second cell has a diameter of 1.5 x 10-5 meters. Which cell has a greater diameter? 4.11 x x > 1.5 Compare the exponents. Compare the values between 1 and 10. Notice that 4.11 x 10-5 > 1.5 x The first cell has a greater diameter.

25 Your Turn: A star has a diameter of approximately 5.11 x 10 3 kilometers. A second star has a diameter of 5 x 10 4 kilometers. Which star has a greater diameter? 5.11 x x 10 4 Compare the exponents. Notice that 3 < 4. So 5.11 x 10 3 < 5 x 10 4 The second star has a greater diameter.

26 Example: Ordering Numbers in Scientific Notation Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10

27 Your Turn: Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of x 10-12, 4 x 10-3, 5.2 x 10-3, 3 x 10 14, 4.5 x 10 14, 4.5 x Step 2 Order the numbers that have the same power of 10

28 Joke Time Did you hear about the red ship and the blue ship that collided? Both crews were marooned! What did one shark say to the other while eating a clownfish? This tastes funny! What did the cobbler say when a cat wandered into his shop? Shoe!

The wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders.

The wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders. Section 6 2A: A common use of positive and negative exponents is writing numbers in scientific notation. In astronomy, the distance between 2 objects can be very large and the numbers often contain many

More information

Scientific Notation and Powers of Ten Calculations

Scientific Notation and Powers of Ten Calculations Appendix A Scientific Notation and Powers of Ten Calculations A.1 Scientific Notation Often the quantities used in chemistry problems will be very large or very small numbers. It is much more convenient

More information

1. The algebra of exponents 1.1. Natural Number Powers. It is easy to say what is meant by a n a (raised to) to the (power) n if n N.

1. The algebra of exponents 1.1. Natural Number Powers. It is easy to say what is meant by a n a (raised to) to the (power) n if n N. CHAPTER 3: EXPONENTS AND POWER FUNCTIONS 1. The algebra of exponents 1.1. Natural Number Powers. It is easy to say what is meant by a n a (raised to) to the (power) n if n N. For example: In general, if

More information

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left. The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

More information

eday Lessons Mathematics Grade 8 Student Name:

eday Lessons Mathematics Grade 8 Student Name: eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards- Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times

More information

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write 4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall

More information

Student Exploration: Unit Conversions

Student Exploration: Unit Conversions Name: Date: Student Exploration: Unit Conversions Vocabulary: base unit, cancel, conversion factor, dimensional analysis, metric system, prefix, scientific notation Prior Knowledge Questions (Do these

More information

Negative Exponents and Scientific Notation

Negative Exponents and Scientific Notation 3.2 Negative Exponents and Scientific Notation 3.2 OBJECTIVES. Evaluate expressions involving zero or a negative exponent 2. Simplify expressions involving zero or a negative exponent 3. Write a decimal

More information

Review of Scientific Notation and Significant Figures

Review of Scientific Notation and Significant Figures II-1 Scientific Notation Review of Scientific Notation and Significant Figures Frequently numbers that occur in physics and other sciences are either very large or very small. For example, the speed of

More information

Linear Equations and Inequalities

Linear Equations and Inequalities Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................

More information

Exponents, Radicals, and Scientific Notation

Exponents, Radicals, and Scientific Notation General Exponent Rules: Exponents, Radicals, and Scientific Notation x m x n = x m+n Example 1: x 5 x = x 5+ = x 7 (x m ) n = x mn Example : (x 5 ) = x 5 = x 10 (x m y n ) p = x mp y np Example : (x) =

More information

2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division

2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division Math Section 5. Dividing Decimals 5. Dividing Decimals Review from Section.: Quotients, Dividends, and Divisors. In the expression,, the number is called the dividend, is called the divisor, and is called

More information

26 Integers: Multiplication, Division, and Order

26 Integers: Multiplication, Division, and Order 26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue

More information

Exponents, Factors, and Fractions. Chapter 3

Exponents, Factors, and Fractions. Chapter 3 Exponents, Factors, and Fractions Chapter 3 Exponents and Order of Operations Lesson 3-1 Terms An exponent tells you how many times a number is used as a factor A base is the number that is multiplied

More information

CONNECT: Ways of writing numbers

CONNECT: Ways of writing numbers CONNECT: Ways of writing numbers SCIENTIFIC NOTATION; SIGNIFICANT FIGURES; DECIMAL PLACES First, a short review of our Decimal (Base 10) System. This system is so efficient that we can use it to write

More information

Operations on Decimals

Operations on Decimals 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. Then write the decimal

More information

Basic Calculations and Percentages

Basic Calculations and Percentages Saturday X-tra X-Sheet: 1 Basic Calculations and Percentages Key Concepts In this session, we will focus on summarising what you need to know about: - Basic Calculations (revision of earlier work) o Scientific

More information

A.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents

A.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify

More information

Fractions and Decimals (pages 62 66)

Fractions and Decimals (pages 62 66) A Fractions and Decimals (pages 6 66) A decimal that ends, such as 0., is a terminating decimal. All terminating decimals are rational numbers. 0.,000 A decimal that repeats, such as 0. is a repeating

More information

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman hundredths tenths ones tens Decimal Art An Introduction to Decimals Directions: Part 1: Coloring Have children

More information

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

More information

Emily is taking an astronomy course and read the following in her textbook:

Emily is taking an astronomy course and read the following in her textbook: 6. EXPONENTS Emily is taking an astronomy course and read the following in her textbook: The circumference of the Earth (the distance around the equator) is approximately.49 0 4 miles. Emily has seen scientific

More information

2.2 Scientific Notation: Writing Large and Small Numbers

2.2 Scientific Notation: Writing Large and Small Numbers 2.2 Scientific Notation: Writing Large and Small Numbers A number written in scientific notation has two parts. A decimal part: a number that is between 1 and 10. An exponential part: 10 raised to an exponent,

More information

Grade 6 Math Circles. Exponents

Grade 6 Math Circles. Exponents Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles November 4/5, 2014 Exponents Quick Warm-up Evaluate the following: 1. 4 + 4 + 4 +

More information

DECIMALS are special fractions whose denominators are powers of 10.

DECIMALS are special fractions whose denominators are powers of 10. DECIMALS 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 decimals. The

More information

Grade 7/8 Math Circles October 7/8, Exponents and Roots - SOLUTIONS

Grade 7/8 Math Circles October 7/8, Exponents and Roots - SOLUTIONS Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 7/8, 2014 Exponents and Roots - SOLUTIONS This file has all the missing

More information

MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

More information

Negative Integral Exponents. If x is nonzero, the reciprocal of x is written as 1 x. For example, the reciprocal of 23 is written as 2

Negative Integral Exponents. If x is nonzero, the reciprocal of x is written as 1 x. For example, the reciprocal of 23 is written as 2 4 (4-) Chapter 4 Polynomials and Eponents P( r) 0 ( r) dollars. Which law of eponents can be used to simplify the last epression? Simplify it. P( r) 7. CD rollover. Ronnie invested P dollars in a -year

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

Rule 2: If the decimal point is moved to the left, the exponent is positive.

Rule 2: If the decimal point is moved to the left, the exponent is positive. Scientific Notation Any quantity can be expressed using a power of ten. As you move the decimal point, you multiply by 10 as many times as necessary to make the numbers equal. Consider the following examples:

More information

Rules for Exponents and the Reasons for Them

Rules for Exponents and the Reasons for Them Print this page Chapter 6 Rules for Exponents and the Reasons for Them 6.1 INTEGER POWERS AND THE EXPONENT RULES Repeated addition can be expressed as a product. For example, Similarly, repeated multiplication

More information

Roots of Real Numbers

Roots of Real Numbers Roots of Real Numbers Math 97 Supplement LEARNING OBJECTIVES. Calculate the exact and approximate value of the square root of a real number.. Calculate the exact and approximate value of the cube root

More information

Exponents. Exponents tell us how many times to multiply a base number by itself.

Exponents. Exponents tell us how many times to multiply a base number by itself. Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,

More information

PREPARATION FOR MATH TESTING at CityLab Academy

PREPARATION FOR MATH TESTING at CityLab Academy PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRE-TEST

More information

Chapter 1. An Introduction to Chemistry By Mark Bishop

Chapter 1. An Introduction to Chemistry By Mark Bishop Chapter 1 An Introduction to Chemistry By Mark Bishop Chemistry The science that deals with the structure and behavior of matter Summary of Study Strategies The will to succeed is important, but what s

More information

Quick Reference ebook

Quick Reference ebook This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

More information

CHAPTER 4 DIMENSIONAL ANALYSIS

CHAPTER 4 DIMENSIONAL ANALYSIS CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.

More information

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers. Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

More information

Name Date Block. Algebra 1 Laws of Exponents/Polynomials Test STUDY GUIDE

Name Date Block. Algebra 1 Laws of Exponents/Polynomials Test STUDY GUIDE Name Date Block Know how to Algebra 1 Laws of Eponents/Polynomials Test STUDY GUIDE Evaluate epressions with eponents using the laws of eponents: o a m a n = a m+n : Add eponents when multiplying powers

More information

Chapter 2 Formulas and Decimals

Chapter 2 Formulas and Decimals Chapter Formulas and Decimals Section A Rounding, Comparing, Adding and Subtracting Decimals Look at the following formulas. The first formula (P = A + B + C) is one we use to calculate perimeter of a

More information

1. Give the 16 bit signed (twos complement) representation of the following decimal numbers, and convert to hexadecimal:

1. Give the 16 bit signed (twos complement) representation of the following decimal numbers, and convert to hexadecimal: Exercises 1 - number representations Questions 1. Give the 16 bit signed (twos complement) representation of the following decimal numbers, and convert to hexadecimal: (a) 3012 (b) - 435 2. For each of

More information

Multiplying and Dividing Fractions

Multiplying and Dividing Fractions Multiplying and Dividing Fractions 1 Overview Fractions and Mixed Numbers Factors and Prime Factorization Simplest Form of a Fraction Multiplying Fractions and Mixed Numbers Dividing Fractions and Mixed

More information

After adjusting the expoent value of the smaller number have

After adjusting the expoent value of the smaller number have 1 (a) Provide the hexadecimal representation of a denormalized number in single precision IEEE 754 notation. What is the purpose of denormalized numbers? A denormalized number is a floating point number

More information

Binary Number System. 16. Binary Numbers. Base 10 digits: 0 1 2 3 4 5 6 7 8 9. Base 2 digits: 0 1

Binary Number System. 16. Binary Numbers. Base 10 digits: 0 1 2 3 4 5 6 7 8 9. Base 2 digits: 0 1 Binary Number System 1 Base 10 digits: 0 1 2 3 4 5 6 7 8 9 Base 2 digits: 0 1 Recall that in base 10, the digits of a number are just coefficients of powers of the base (10): 417 = 4 * 10 2 + 1 * 10 1

More information

Binary math. Resources and methods for learning about these subjects (list a few here, in preparation for your research):

Binary math. Resources and methods for learning about these subjects (list a few here, in preparation for your research): Binary math This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

More information

Introduction to Fractions

Introduction to Fractions Introduction to Fractions Fractions represent parts of a whole. The top part of a fraction is called the numerator, while the bottom part of a fraction is called the denominator. The denominator states

More information

Solution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2

Solution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2 5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square

More information

Zero and Negative Exponents. Section 7-1

Zero and Negative Exponents. Section 7-1 Zero and Negative Exponents Section 7-1 Goals Goal To simplify expressions involving zero and negative exponents. Rubric Level 1 Know the goals. Level 2 Fully understand the goals. Level 3 Use the goals

More information

Student Outcomes. Lesson Notes. Classwork. Discussion (10 minutes)

Student Outcomes. Lesson Notes. Classwork. Discussion (10 minutes) NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 8 Student Outcomes Students know the definition of a number raised to a negative exponent. Students simplify and write equivalent expressions that contain

More information

Grade 6 Math Circles. Binary and Beyond

Grade 6 Math Circles. Binary and Beyond Faculty of Mathematics Waterloo, Ontario N2L 3G1 The Decimal System Grade 6 Math Circles October 15/16, 2013 Binary and Beyond The cool reality is that we learn to count in only one of many possible number

More information

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality. 8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent

More information

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

More information

Integers, I, is a set of numbers that include positive and negative numbers and zero.

Integers, I, is a set of numbers that include positive and negative numbers and zero. Grade 9 Math Unit 3: Rational Numbers Section 3.1: What is a Rational Number? Integers, I, is a set of numbers that include positive and negative numbers and zero. Imagine a number line These numbers are

More information

INTRODUCTORY CHEMISTRY Concepts and Critical Thinking

INTRODUCTORY CHEMISTRY Concepts and Critical Thinking INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Sixth Edition by Charles H. Corwin Scientific Measurements by Christopher Hamaker 1 Uncertainty in Measurements A measurement is a number with a unit

More information

Chapter 1 Lecture Notes: Science and Measurements

Chapter 1 Lecture Notes: Science and Measurements Educational Goals Chapter 1 Lecture Notes: Science and Measurements 1. Explain, compare, and contrast the terms scientific method, hypothesis, and experiment. 2. Compare and contrast scientific theory

More information

Sect Exponents: Multiplying and Dividing Common Bases

Sect Exponents: Multiplying and Dividing Common Bases 40 Sect 5.1 - Exponents: Multiplying and Dividing Common Bases Concept #1 Review of Exponential Notation In the exponential expression 4 5, 4 is called the base and 5 is called the exponent. This says

More information

Calculation of Exponential Numbers

Calculation of Exponential Numbers Calculation of Exponential Numbers Written by: Communication Skills Corporation Edited by: The Science Learning Center Staff Calculation of Exponential Numbers is a written learning module which includes

More information

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have 8.6 Rational Exponents 8.6 OBJECTIVES 1. Define rational exponents 2. Simplify expressions containing rational exponents 3. Use a calculator to estimate the value of an expression containing rational exponents

More information

Math. Fraction, Decimal & Percent (Visual) Answers. Name: Determine the value written as a fraction, decimal & a percent. Ex) Fraction.

Math. Fraction, Decimal & Percent (Visual) Answers. Name: Determine the value written as a fraction, decimal & a percent. Ex) Fraction. , Decimal & Percent (Visual) ) ) 0. 0%. 0. % ) Decimal 0. Percent 0% Decimal 0. Percent % ) Decimal 0. Percent %... 0. % 0. 0% 0. % 0. %. 0. %. 0. 0% ) Decimal 0. Percent 0% ) Decimal 0. Percent % ) Decimal

More information

Number Systems and Base Conversions

Number Systems and Base Conversions Number Systems and Base Conversions As you know, the number system that we commonly use is the decimal or base- 10 number system. That system has 10 digits, 0 through 9. While it's very convenient for

More information

The gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.

The gas can has a capacity of 4.17 gallons and weighs 3.4 pounds. hundred million$ ten------ million$ million$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.

More information

Introduction to Powers of 10

Introduction to Powers of 10 Introduction to Powers of 10 Topics Covered in This Chapter: I-1: Scientific Notation I-2: Engineering Notation and Metric Prefixes I-3: Converting between Metric Prefixes I-4: Addition and Subtraction

More information

EXERCISE # 1.Metric Measurement & Scientific Notation

EXERCISE # 1.Metric Measurement & Scientific Notation EXERCISE # 1.Metric Measurement & Scientific Notation Student Learning Outcomes At the completion of this exercise, students will be able to learn: 1. How to use scientific notation 2. Discuss the importance

More information

Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together

Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a

More information

Session 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers:

Session 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers: Session 9 Scientific Notation and Laws of Exponents If you have ever taken a Chemistry class, you may have encountered the following numbers: There are approximately 60,4,79,00,000,000,000,000 molecules

More information

Property: Rule: Example:

Property: Rule: Example: Math 1 Unit 2, Lesson 4: Properties of Exponents Property: Rule: Example: Zero as an Exponent: a 0 = 1, this says that anything raised to the zero power is 1. Negative Exponent: Multiplying Powers with

More information

a b Grade 6 Math Circles Fall 2010 Exponents and Binary Numbers Powers What is the product of three 2s? =

a b Grade 6 Math Circles Fall 2010 Exponents and Binary Numbers Powers What is the product of three 2s? = 1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Powers What is the product of three 2s? 2 2 2 = What is the product of five 2s? 2 2 2 2 2 = Grade 6 Math

More information

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the

More information

5th Grade Unit 1: Whole Number and Decimal Fraction Place Value to the One Thousandths (4 Weeks)

5th Grade Unit 1: Whole Number and Decimal Fraction Place Value to the One Thousandths (4 Weeks) 5th Grade Unit : Whole Number and Decimal Fraction Place Value to the One Thousandths (4 Weeks) Stage Desired Results Established Goals Unit Description Students continue to extend and apply their understanding

More information

MATH Fundamental Mathematics II.

MATH Fundamental Mathematics II. MATH 10032 Fundamental Mathematics II http://www.math.kent.edu/ebooks/10032/fun-math-2.pdf Department of Mathematical Sciences Kent State University December 29, 2008 2 Contents 1 Fundamental Mathematics

More information

Binary Numbers. Binary Octal Hexadecimal

Binary Numbers. Binary Octal Hexadecimal Binary Numbers Binary Octal Hexadecimal Binary Numbers COUNTING SYSTEMS UNLIMITED... Since you have been using the 10 different digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 all your life, you may wonder how

More information

Preparation for BioScience Academy Math Assessment Test

Preparation for BioScience Academy Math Assessment Test Preparation for BioScience Academy Math Assessment Test Math is an essential component of laboratory science and solid math skills are required for a successful career in this field. To be eligible for

More information

Introduction to IEEE Standard 754 for Binary Floating-Point Arithmetic

Introduction to IEEE Standard 754 for Binary Floating-Point Arithmetic Introduction to IEEE Standard 754 for Binary Floating-Point Arithmetic Computer Organization and Assembly Languages, NTU CSIE, 2004 Speaker: Jiun-Ren Lin Date: Oct 26, 2004 Floating point numbers Integers:

More information

SCIENTIFIC MEASUREMENT

SCIENTIFIC MEASUREMENT 3 SCIENTIFIC MEASUREMENT Conceptual Curriculum Concrete concepts More abstract concepts or math/problem-solving Standard Curriculum Core content Extension topics Honors Curriculum Core honors content Options

More information

Rational Exponents. Given that extension, suppose that. Squaring both sides of the equation yields. a 2 (4 1/2 ) 2 a 2 4 (1/2)(2) a a 2 4 (2)

Rational Exponents. Given that extension, suppose that. Squaring both sides of the equation yields. a 2 (4 1/2 ) 2 a 2 4 (1/2)(2) a a 2 4 (2) SECTION 0. Rational Exponents 0. OBJECTIVES. Define rational exponents. Simplify expressions with rational exponents. Estimate the value of an expression using a scientific calculator. Write expressions

More information

NUMBER SYSTEMS. William Stallings

NUMBER SYSTEMS. William Stallings NUMBER SYSTEMS William Stallings The Decimal System... The Binary System...3 Converting between Binary and Decimal...3 Integers...4 Fractions...5 Hexadecimal Notation...6 This document available at WilliamStallings.com/StudentSupport.html

More information

5.1 Radical Notation and Rational Exponents

5.1 Radical Notation and Rational Exponents Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots

More information

CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME!

CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! You may have come across the terms powers, indices, exponents and logarithms. But what do they mean? The terms power(s),

More information

4 Solving Systems of Equations by Reducing Matrices

4 Solving Systems of Equations by Reducing Matrices Math 15 Sec S0601/S060 4 Solving Systems of Equations by Reducing Matrices 4.1 Introduction One of the main applications of matrix methods is the solution of systems of linear equations. Consider for example

More information

Algebra Course KUD. Green Highlight - Incorporate notation in class, with understanding that not tested on

Algebra Course KUD. Green Highlight - Incorporate notation in class, with understanding that not tested on Algebra Course KUD Yellow Highlight Need to address in Seminar Green Highlight - Incorporate notation in class, with understanding that not tested on Blue Highlight Be sure to teach in class Postive and

More information

PHYSICS 151 Notes for Online Lecture #1

PHYSICS 151 Notes for Online Lecture #1 PHYSICS 151 Notes for Online Lecture #1 Whenever we measure a quantity, that measurement is reported as a number and a unit of measurement. We say such a quantity has dimensions. Units are a necessity

More information

A Short Guide to Significant Figures

A Short Guide to Significant Figures A Short Guide to Significant Figures Quick Reference Section Here are the basic rules for significant figures - read the full text of this guide to gain a complete understanding of what these rules really

More information

Decimal and Fraction Review Sheet

Decimal and Fraction Review Sheet Decimal and Fraction Review Sheet Decimals -Addition To add 2 decimals, such as 3.25946 and 3.514253 we write them one over the other with the decimal point lined up like this 3.25946 +3.514253 If one

More information

Year Five Maths Notes

Year Five Maths Notes Year Five Maths Notes NUMBER AND PLACE VALUE I can count forwards in steps of powers of 10 for any given number up to 1,000,000. I can count backwards insteps of powers of 10 for any given number up to

More information

Decimal Notation ,000 10, Write a word name for the whole number. That is, the number to the left of the decimal point.

Decimal Notation ,000 10, Write a word name for the whole number. That is, the number to the left of the decimal point. Decimal Notation Place Value Chart Hundreds Tens Ones Tenths Hundredths Thousandths Ten- Thousandths 00 0 0 00,000 0, 000 Hundred- Thousandths 00, 000 Millionths,000, 000 How to write a word name, given

More information

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials Algebra Unit 6 Syllabus revised /7/13 1 Objective: Multiply monomials. Simplify expressions involving powers of monomials. Pre-assessment: Exponents, Fractions, and Polynomial Expressions Lesson: Pages

More information

Week 1, Lesson 1 1. Plan for Success 2. ICA Rules & Procedures

Week 1, Lesson 1 1. Plan for Success 2. ICA Rules & Procedures What do you need to know in order to be successful in class this year? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question

More information

HOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9

HOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9 HOSPITALITY Math Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George

More information

A physical quantity is any quantity that can be measured with a certain mathematical precision. Example: Force

A physical quantity is any quantity that can be measured with a certain mathematical precision. Example: Force 1 Unit Systems Conversions Powers of Physical Quantities Dimensions Dimensional Analysis Scientific Notation Computer Notation Calculator Notation Significant Figures Math Using Significant Figures Order

More information

Algebra 1A and 1B Summer Packet

Algebra 1A and 1B Summer Packet Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the

More information

Section R.2. Fractions

Section R.2. Fractions Section R.2 Fractions Learning objectives Fraction properties of 0 and 1 Writing equivalent fractions Writing fractions in simplest form Multiplying and dividing fractions Adding and subtracting fractions

More information

Anchorage School District/Alaska Sr. High Math Performance Standards Algebra

Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,

More information

COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13

COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13 COMPASS Numerical Skills/Pre-Algebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre

More information

Lab 1: Units and Conversions

Lab 1: Units and Conversions Lab 1: Units and Conversions The Metric System In order to measure the properties of matter, it is necessary to have a measuring system and within that system, it is necessary to define some standard dimensions,

More information

Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

More information

Chapter 3 Review Math 1030

Chapter 3 Review Math 1030 Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%

More information

Student Outcomes. Lesson Notes. Classwork. Exercises 1 and 2 (3 minutes) Socratic Discussion (3 minutes)

Student Outcomes. Lesson Notes. Classwork. Exercises 1 and 2 (3 minutes) Socratic Discussion (3 minutes) Student Outcomes Students continue to practice working with very small and very large numbers expressed in scientific notation. Students read, write, and perform operations on numbers expressed in scientific

More information

Unit 1: Place Value/Multiplication/ Division of Whole Numbers

Unit 1: Place Value/Multiplication/ Division of Whole Numbers Unit 1: Place Value/Multiplication/ Division of Whole Numbers Learning Targets: LT1. Represent the value of a number multiplied or divided by a power of ten with a number line, base ten block, and drawing.

More information

MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume.

MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume. MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume For prisms, pyramids, cylinders, and cones: Volume is the area of one base

More information

Simplifying Fractions

Simplifying Fractions . Simplifying Fractions. OBJECTIVES 1. Determine whether two fractions are equivalent. Use the fundamental principle to simplify fractions It is possible to represent the same portion of the whole by different

More information