# Calculation of Exponential Numbers

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 practice problems and a posttest (obtained in the Science Learning Center).

2 The objectives are to learn to: 1) convert numbers to standard exponential numbers, 2) change the exponent of a number to a higher or lower value without changing the magnitude of the exponential number, and 3) add, subtract, multiply and divide exponential numbers with your answer having the correct number of significant figures.

3 Before attempting this module, be sure you understand: 1. The conversion of decimal numbers to standard exponential notation. 2. How to add, subtract, multiply and divide regular numbers with your answer having the correct number of significant figures. We will briefly review (1) and (2) in the next few slides.

4 Review Conversion of Decimal Numbers to Standard Exponential Notation On the next slide, the number 1,234 is shown in six forms. The value of each form is the same. As the decimal point is moved to the left, the value of the exponent increases by one for each move. The standard exponential form of this number is x In this form the pre-exponential number is between one and ten. (To add and subtract exponents, it is frequently necessary to change the form of one or more numbers)

5 x Review Conversion of Decimal Numbers to Standard Exponential Notation x x ,234 = x x x x 10 4 Standard Exponential Form

6 Review Conversion of Decimal Numbers to Standard Exponential Notation x 10-3 has a negative exponent. It can be changed to x 10-2 which is a larger exponent, by using the same process. Remember 10-2 is greater than This is shown on the next slide.

7 ADD ONE x 10 4 = ^1.234 x = x 10 5 MOVE ONE ADD ONE x 10-3 = ^1.234 x = x 10-2 MOVE ONE Remember 10-2 is greater than (>) 10-3

8 SUBTRACT ONE x 10 5 = 1.2^34 x = x 10 4 MOVE ONE SUBTRACT ONE x 10-3 = 1.2^34 x = x 10-4 MOVE ONE

9 Now, it is your turn to attempt some problems like these. Complete the problems below. The answers are on the next slide. Problem Set 1 Part A Insert the correct value of the exponent in place of the (?) question mark. = 8,765.4 x 10? (a) 87,654 = x 10? (b) = x 10? (c) Identify which of the above answers, a, b, or c, is in standard exponential form. Part B What is the correct value of the pre-exponential number? x 10-4 =? x 10-3 =? x 10-1 Part C Insert the correct value of the exponent in place of the question mark (?). 6,666.0 = x 10? = x 10? Part D Insert the correct value of the exponent in place of the question mark (?) = x 10? = x 10?

10 Solutions to Problem Set 1 Part A Insert the correct value of the exponent in place of the (?) question mark. = 8,765.4 x 10 1 (a) 87,654 = x 10 2 (b) = x 10 4 (c) Identify which of the above answers, a, b, or c, is in standard exponential form. Answer c ( x 10 4 ) is in standard exponential form. Part B What is the correct value of the pre-exponential number? x 10-4 = x 10-3 = x 10-1 Part C Insert the correct value of the exponent in place of the question mark (?). 6,666.0 = x 10 3 = x 10 5 Part D Insert the correct value of the exponent in place of the question mark (?) = x 10-3 = x 10 2

11 Review Rules for Significant Figures Addition/ subtraction Determine which number in the calculations has the least number of digits to the right of the decimal point. Your result will also have the same number of digits to the right of the decimal point Result: Multiplication / Division Rounding Answer Determine which number in the calculations has the least total number of significant figures (regardless of the decimal point s position). Your result will also have that same number of significant figures. When you are doing several calculations, carry out all calculations to at least one more significant figure than you need. When you get the final result, then round off to the correct number of significant figures x Result: x 1610 = / 3600 = Result: 25

12 Now that we have briefly reviewed 1. Conversion of decimal numbers to standard exponential numbers and 2. Rules for significant figures We can proceed with the rest of the module on Calculating with Exponential Numbers

13 Addition and Subtraction of Exponential Numbers To add two exponential numbers you must first convert the exponents to the same value. It is best to change the exponent of the smaller number to that of the larger number. In this example we will add 1.2 x 10 4 to 3.4 x Using the rule, we first change the lower exponent to Both numbers will now have the same exponent: 0.12 x 10 5 and 3.4 x We now add the preexponential numbers 0.12 and 3.4. Our answer is 3.52 x 10 5 which is rounded to 3.5 x 10 5.

14 ADDING TWO EXPONENTIAL NUMBERS: convert exponents to same value best to change exponent of the smaller number to that of the larger number. EXAMPLE: (1.2 x 10 4 ) + (3.4 x 10 5 ) ADD ONE ^1.2 x =5 MOVE ONE (0.12 x 10 5 ) + ( ) ( ) x 10 5 = 3.52 x 10 5 round to 3.5 x 10 5 (2 significant figures)

15 SUBTRACTING TWO EXPONENTIAL NUMBERS: Again convert to the same exponent by changing the value of the lower exponent to that of the higher exponent. EXAMPLE: (3.4 x 10 5 ) - (1.2 x 10 4 ) = ADD ONE ^1.2 x =5 MOVE ONE ( ) x 10 5 = 3.28 x 10 5 round to 3.3 x 10 5 (2 significant figures)

16 ADDITION AND SUBTRACTION OF EXPONENTIAL NUMBERS WITH NEGATIVE EXPONENTS REMEMBER - THE SMALLER THE EXPONENT, THE LARGER THE NUMBER. THUS: (1.2 x 10-6 ) + (3.2 x 10-7 ) = ADD ONE ^3.2 x =-6 MOVE ONE = ( ) x 10-6 = 1.52 x 10-6 round to 1.5 x 10-6 (2 significant figures) TO SUBTRACT: (5.6 x 10-6 ) - (3.4 x 10-7 ) ADD ONE ^3.4 x =-6 MOVE ONE = ( ) x 10-6 = 5.26 x 10-6 round to 5.3 x 10-6 (2 significant figures)

17 Now, it is your turn to attempt some problems like these. Complete the problems below. The answers are on the next slide. Problem Set 2 Add or subtract the following exponential numbers. Express all your answers in standard exponential form. (a) x x 10 5 =? (b) x x 10 3 =? (c) 1.72 x x 10-5 =? (d) 8.12 x x 10 6 =? (e) 6.21 x x 10-4 =? (f) x x 10-1 =? (g) 3.14 x x =? (h) =? HINT: Write 10 5 as 1.0 x 10 5, and 10 4 as 1.0 x 10 4 )

18 Solutions to Problem Set 2 Add or subtract the following exponential numbers. Express all your answers in standard exponential form. (a) x x 10 5 = x 10 5 round to 6.10 x 10 5 (b) x x 10 3 = x 10 4 (c) 1.72 x x 10-5 = x 10-4 round to 1.93 x 10-4 (d) 8.12 x x 10 6 = x 10 8 round to 8.13 x 10 8 (e) 6.21 x x 10-4 = x 10-2 round to 6.19 x 10-2 (f) x x 10-1 = x 10 2 (g) 3.14 x x = 3.12 x 10-9 (h) = 9.0 x 10 4

19 Multiplication and Division of Exponential Numbers Now let s consider the multiplication of exponentials. First we will consider an example using simple exponentials such as 10 2 times is 10x10 and 10 3 is 10x10x10; multiply together to get 10 x 10 x 10 x 10 x10. Thus 10 2 times 10 3 is 10 5 which is the sum of the two exponents 2 plus 3 or 10 (2 + 3).

20 EXAMPLE = 10 2 x x 10 3 =? = (10 x 10) x (10 x 10 x 10) = 10 x 10 x 10 x 10 x 10 = 10 5 ( )

21 MULTIPLYING EXPONENTIALS ADD EXPONENTS 10 2 x 10 3 = 10 (2 + 3) = x 10 7 x 10 2 = 10 ( ) = 10 13

22 DIVIDING EXPONENTIALS SUBTRACT EXPONENT OF DENOMINATOR EXAMPLE: 10 5 /10 2 = 10 3 (DIFFERENCE 5-2=3) DIVIDE = 10 x 10 x 10 x 10 x x 10 =10 3

23 SIMPLIFYING THE DIVISION OF A NEGATIVE EXPONETIAL The division of exponentials can be simplified by recalling that a negative exponent can be written as the reciprocal of that number. 1/10 2 is the same as Thus 10 5 divided by 10 2 equals 10 5 x 1/10 2 or 10 5 x To multiply, we add exponents. 10 (5-2) is RECIPROCAL = 10-2 THUS 10 5 = 10 5 x 1 = 10 5 x TO MULTIPLY = 10 (5-2) = 10 3

24 Using the previous example we can simplify exponential expressions. The following is an example combining multiplication and division, which can be reduced to a simple addition problem. (10 4 x 10 7 )/(10-2 x 10 3 ) =? 10 4 x x 10 3 = 10 4 x 10 7 x 10 2 x 10-3 = 10 ( ) - 3 = 10 10

25 Now, it is your turn to attempt some problems like these. Complete the problems below. The answers are on the next slide. Problem Set 3 Complete the following expressions 1) 10 2 x 10 3 =? 2) 10 2 x 10 3 x 10 6 =? 3) 10 5 /10 4 =? 4) 10 2 /10-1 =? 5) 10 5 x 10-2 =? 6) 10 5 x 10 6 x 10-3 =? 7) (10 8 x 10 4 )/10-2 =? 8) (10 7 x 10 3 )/(10-2 x 10 4 ) =? 9) (10-5 )/(10-2 x 10 4 x 10-6 ) =? 10) /10-10 =?

26 Solutions to Problem Set 3 1) 10 2 x 10 3 = ) 10 2 x 10 3 x 10 6 = ) 10 5 /10 4 = 10 or ) 10 2 /10-1 = ) 10 5 x 10-2 = ) 10 5 x 10 6 x 10-3 = ) (10 8 x 10 4 )/10-2 = ) (10 7 x 10 3 )/(10-2 x 10 4 ) = ) (10-5 )/(10-2 x 10 4 x 10-6 ) = ) /10-10 = 10-2

27 MULTIPLICATION OF COMPLEX EXPONENTIAL NUMBERS EXAMPLE: (1.2 x 10 3 ) x (1.2 x 10 5 ) STEP 1 (1.2 x 1.2) x x (10 3 x 10 5 ) STEP x ( ) = 1.44 x 10 8 round to 1.4 x significant figures

28 DIVISION OF COMPLEX EXPONENTIAL NUMBERS EXAMPLE: (4.8 x 10 4 ) (1.2 x 10 2 ) STEP x 1.2 STEP 2 10 x x = 4.0 x 10 2

29 SOLVING MORE COMPLICATED EXPRESSIONS (1.2 x 10 4 ) x (2.0 x 10-2 ) (4.0 x 10-3 ) x (6.0 x 10 2 ) SEPARATE = DECIMALS EXPONENTS 1.2 x x 6.0 x 10 4 x x 10 2 = 0.10 x ( ) 10 = 0.10 x 10 3 = 1.0 x 10 2 (Standard Exponential Form )

30 Now, it is your turn to attempt some problems like these. Complete the problems below. The answers are on the next slide. Problem Set 4 Complete the following expressions. Express all your answers in standard exponential form. 1) (1.2 x 10 4 ) x (2.0 x 10 3 ) =? 2) (1.1 x 10-4 ) x (3.0 x 10 7 ) =? 3) (4.2 x 10 5 )/(3.0 x 10 3 ) =? 4) (4.2 x )/(3.0 x 10-4 ) =? 5) [(1.44 x 10-4 ) x (2.0 x 10 6 )]/(1.2 x 10-3 ) =? 6) [(4.6 x 10 6 ) x (2.2 x 10-5 )]/[(1.1 x 10 4 ) x (2.3 x 10-7 )] =? 7) (5.6 x 10-5 )/[(8.0 x 10-2 ) x (7.0 x 10 7 )] =?

31 Solutions to Problem Set 4 Complete the following expressions. Express all your answers in standard exponential form. 1) (1.2 x 10 4 ) x (2.0 x 10 3 ) = 2.4 x ) (1.1 x 10-4 ) x (3.0 x 10 7 ) = 3.3 x ) (4.2 x 10 5 )/(3.0 x 10 3 ) = 1.4 x ) (4.2 x )/(3.0 x 10-4 ) =1.4 x ) [(1.44 x 10-4 ) x (2.0 x 10 6 )]/(1.2 x 10-3 ) = 2.4 x ) [(4.6 x 10 6 ) x (2.2 x 10-5 )]/[(1.1 x 10 4 ) x (2.3 x 10-7 )] = 4.0 x ) (5.6 x 10-5 )/[(8.0 x 10-2 ) x (7.0 x 10 7 )] = 1.0 x 10-11

32 RULES: ADDITION AND SUBTRACTION Rule One: Both exponentials must have the same exponent. Rule Two: Transform the exponent of the smaller number to that of the larger number. Rule Three: Carry out addition or subtraction multiply by the common exponent.

33 REVIEW Multiplication Division Add Exponents Subtract Exponent

34 REVIEW MULTIPLICATION Example: (4.0 x 10 2 ) x (2.0 x 10 6 ) = (4.0 x 2.0) x (10 2 x 10 6 ) = 8. 0 x 10 8 DIVISION Example: 4.0 x x 10 6 = 4.0 x 10 2 = = 2.0 x = 2.0 x 10-4

35 Take the Posttest! You are now finished with this module. If you haven't already done the practice problems, we recommend you try them. When you're done, obtain a posttest from the Science Learning Center personnel and complete it.

### 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

### 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

### 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

### Fractions to decimals

Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of

### Roots and Powers. Written by: Bette Kreuz Edited by: Science Learning Center Staff

Roots and Powers Written by: Bette Kreuz Edited by: Science Learning Center Staff The objectives for this module are to: 1. Raise exponential numbers to a power. 2. Extract the root of an exponential number.

### 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

### 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

### Solving Logarithmic Equations

Solving Logarithmic Equations Deciding How to Solve Logarithmic Equation When asked to solve a logarithmic equation such as log (x + 7) = or log (7x + ) = log (x + 9), the first thing we need to decide

### Solving Exponential Equations

Solving Exponential Equations Deciding How to Solve Exponential Equations When asked to solve an exponential equation such as x + 6 = or x = 18, the first thing we need to do is to decide which way is

### 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

### Exponent Properties Involving Products

Exponent Properties Involving Products Learning Objectives Use the product of a power property. Use the power of a product property. Simplify expressions involving product properties of exponents. Introduction

### Chapter 4 Fractions and Mixed Numbers

Chapter 4 Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers Parts of a Fraction Whole numbers are used to count whole things. To refer to a part of a whole, fractions are used.

### 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

### Accuplacer Arithmetic Study Guide

Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole

### 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

### 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

### 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) =

8. Radicals - Rational Exponents Objective: Convert between radical notation and exponential notation and simplify expressions with rational exponents using the properties of exponents. When we simplify

### Improper Fractions and Mixed Numbers

This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All

### Section 1.9 Algebraic Expressions: The Distributive Property

Section 1.9 Algebraic Expressions: The Distributive Property Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Apply the Distributive Property.

### 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

### 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

### Solutions of Linear Equations in One Variable

2. Solutions of Linear Equations in One Variable 2. OBJECTIVES. Identify a linear equation 2. Combine like terms to solve an equation We begin this chapter by considering one of the most important tools

### 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

### Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

### 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

### FRACTIONS COMMON MISTAKES

FRACTIONS COMMON MISTAKES 0/0/009 Fractions Changing Fractions to Decimals How to Change Fractions to Decimals To change fractions to decimals, you need to divide the numerator (top number) by the denominator

### Self-Directed Course: Transitional Math Module 2: Fractions

Lesson #1: Comparing Fractions Comparing fractions means finding out which fraction is larger or smaller than the other. To compare fractions, use the following inequality and equal signs: - greater than

### 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

### Appendix A: 20 Items and Their Associated 80 Solution Strategies, Proportion Correct Scores, Proportion of Students Selecting the Solution Strategies

Appendix A: 20 Items and Their Associated 80 Solution Strategies, Correct Scores, of Students Selecting the Solution Strategies Table A1. Math Test Items with Associated Strategies and Summaries of Student

### Chapter 15 Radical Expressions and Equations Notes

Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify

### MATH-0910 Review Concepts (Haugen)

Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,

### 1.1. Basic Concepts. Write sets using set notation. Write sets using set notation. Write sets using set notation. Write sets using set notation.

1.1 Basic Concepts Write sets using set notation. Objectives A set is a collection of objects called the elements or members of the set. 1 2 3 4 5 6 7 Write sets using set notation. Use number lines. Know

### 2.6 Exponents and Order of Operations

2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated

### 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

### Lesson Plan -- Rational Number Operations

Lesson Plan -- Rational Number Operations Chapter Resources - Lesson 3-12 Rational Number Operations - Lesson 3-12 Rational Number Operations Answers - Lesson 3-13 Take Rational Numbers to Whole-Number

### Practice Math Placement Exam

Practice Math Placement Exam The following are problems like those on the Mansfield University Math Placement Exam. You must pass this test or take MA 0090 before taking any mathematics courses. 1. What

### Recall the process used for adding decimal numbers. 1. Place the numbers to be added in vertical format, aligning the decimal points.

2 MODULE 4. DECIMALS 4a Decimal Arithmetic Adding Decimals Recall the process used for adding decimal numbers. Adding Decimals. To add decimal numbers, proceed as follows: 1. Place the numbers to be added

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 8 Powers and Exponents

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 8 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

### Now that we have a handle on the integers, we will turn our attention to other types of numbers.

1.2 Rational Numbers Now that we have a handle on the integers, we will turn our attention to other types of numbers. We start with the following definitions. Definition: Rational Number- any number that

Addition with regrouping (carrying) tens 10's ones 1's Put the tens guy up in the tens column... Put the ones guy in the ones answer spot Subtraction with regrouping (borrowing) Place Value Chart Place

### Scientific Measurement

Scientific Measurement How do you measure a photo finish? 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.

### Fractions and Linear Equations

Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

### Algebra 1: Topic 1 Notes

Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating

### DECIMAL REVIEW. 2. Change to a fraction Notice that =.791 The zero in front of the decimal place is not needed.

DECIMAL REVIEW A. INTRODUCTION TO THE DECIMAL SYSTEM The Decimal System is another way of expressing a part of a whole number. A decimal is simply a fraction with a denominator of 10, 100, 1 000 or 10

### Round to Decimal Places

Day 1 1 Round 5.0126 to 2 decimal 2 Round 10.3217 to 3 decimal 3 Round 0.1371 to 3 decimal 4 Round 23.4004 to 2 decimal 5 Round 8.1889 to 2 decimal 6 Round 9.4275 to 2 decimal 7 Round 22.8173 to 1 decimal

### troduction to Algebra

Chapter Five Decimals Section 5.1 Introduction to Decimals Like fractional notation, decimal notation is used to denote a part of a whole. Numbers written in decimal notation are called decimal numbers,

### 3.1. RATIONAL EXPRESSIONS

3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers

### Key. Introduction. What is a Fraction. Better Math Numeracy Basics Fractions. On screen content. Narration voice-over

Key On screen content Narration voice-over Activity Under the Activities heading of the online program Introduction This topic will cover how to: identify and distinguish between proper fractions, improper

### 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

### 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

### Polynomial Identification and Properties of Exponents

2 MODULE 4. INTEGER EXPONENTS AND POLYNOMIALS 4a Polynomial Identification and Properties of Exponents Polynomials We begin with the definition of a term. Term. A term is either a single number (called

### HFCC Math Lab Intermediate Algebra - 7 FINDING THE LOWEST COMMON DENOMINATOR (LCD)

HFCC Math Lab Intermediate Algebra - 7 FINDING THE LOWEST COMMON DENOMINATOR (LCD) Adding or subtracting two rational expressions require the rational expressions to have the same denominator. Example

### Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

### Chapter 1: Order of Operations, Fractions & Percents

HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain

### 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

### 3. Power of a Product: Separate letters, distribute to the exponents and the bases

Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same

### Note: Remember you can always add zeros, after the decimal point, to the back of a number, if needed. \$4.35 \$5.68 \$10.03

5.2 Adding and Subtracting Decimals Adding/Subtracting Decimals. Stack the numbers (one digit on top of another digit). Make sure the decimal points align. 2. Add/Subtract the numbers as if they were whole

### count up and down in tenths count up and down in hundredths

Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number

### 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

### 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

### Addition and Multiplication of Polynomials

LESSON 0 addition and multiplication of polynomials LESSON 0 Addition and Multiplication of Polynomials Base 0 and Base - Recall the factors of each of the pieces in base 0. The unit block (green) is x.

### 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

### Round decimals to the nearest whole number

Round decimals to the nearest whole number Learning Objective Simplifying Fractions Simplified Fractions To simplify a fraction, we find an equivalent fraction which uses the smallest numbers possible.

### Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

### Using the Properties in Computation. a) 347 35 65 b) 3 435 c) 6 28 4 28

(1-) Chapter 1 Real Numbers and Their Properties In this section 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS The properties of the real numbers can be helpful when we are doing computations. In this

### 1.5. section. Arithmetic Expressions

1-5 Exponential Expression and the Order of Operations (1-9) 9 83. 1 5 1 6 1 84. 3 30 5 1 4 1 7 0 85. 3 4 1 15 1 0 86. 1 1 4 4 Use a calculator to perform the indicated operation. Round answers to three

### ARITHMETIC. Overview. Testing Tips

ARITHMETIC Overview The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental

### 2.3. Finding polynomial functions. An Introduction:

2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned

### Let's Review. Adding and Subtracting Polynomials. Remember that Combining Like Terms is an application of the Distributive Property.

Let's Review Adding and Subtracting Polynomials. Combining Like Terms Remember that Combining Like Terms is an application of the Distributive Property. 2x + 3x = (2 + 3)x = 5x 3x 2 + 2x 2 = (3 + 2)x 2

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 9 Order of Operations

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

### Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

### 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.

### Chapter 4 -- Decimals

Chapter 4 -- Decimals \$34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value - 1.23456789

### 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,

### HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers

HFCC Math Lab Arithmetic - Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.

### 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

### Fractions. Cavendish Community Primary School

Fractions Children in the Foundation Stage should be introduced to the concept of halves and quarters through play and practical activities in preparation for calculation at Key Stage One. Y Understand

### Chapter 13: Polynomials

Chapter 13: Polynomials We will not cover all there is to know about polynomials for the math competency exam. We will go over the addition, subtraction, and multiplication of polynomials. We will not

### MULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.

1.4 Multiplication and (1-25) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with

0.7 Quadratic Equations 8 0.7 Quadratic Equations In Section 0..1, we reviewed how to solve basic non-linear equations by factoring. The astute reader should have noticed that all of the equations in that

### comp 180 Lecture 21 Outline of Lecture Floating Point Addition Floating Point Multiplication HKUST 1 Computer Science

Outline of Lecture Floating Point Addition Floating Point Multiplication HKUST 1 Computer Science IEEE 754 floating-point standard In order to pack more bits into the significant, IEEE 754 makes the leading

### 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

### Percentages. It is quite straightforward to convert a percent into a fraction or decimal (and vice versa) using the following rules:

What do percentages mean? Percentages Academic Skills Advice Percent (%) means per hundred. e.g. 22% means 22 per 00, and can also be written as a fraction ( 22 00 ) or a decimal (0.22) It is quite straightforward

### 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

### 6.3 SIMPLIFYING EXPRESSIONS USING THE ORDER OF OPERATIONS

6.3 SIMPLIFYING EXPRESSIONS USING THE ORDER OF OPERATIONS Brian has decided to open a savings account, where he will earn 4% interest, compounded semi-annually. He will deposit \$500 to open the account.

Adding Fractions Adapted from MathisFun.com There are 3 Simple Steps to add fractions: Step 1: Make sure the bottom numbers (the denominators) are the same Step 2: Add the top numbers (the numerators).

### Order of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A.

Order of Operations Section 1: Introduction You know from previous courses that if two quantities are added, it does not make a difference which quantity is added to which. For example, 5 + 6 = 6 + 5.

### SIMPLIFYING SQUARE ROOTS

40 (8-8) Chapter 8 Powers and Roots 8. SIMPLIFYING SQUARE ROOTS In this section Using the Product Rule Rationalizing the Denominator Simplified Form of a Square Root In Section 8. you learned to simplify

### 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

### Order of Operations - PEMDAS. Rules for Multiplying or Dividing Positive/Negative Numbers

Order of Operations - PEMDAS *When evaluating an expression, follow this order to complete the simplification: Parenthesis ( ) EX. (5-2)+3=6 (5 minus 2 must be done before adding 3 because it is in parenthesis.)

### 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

### 3.3 Addition and Subtraction of Rational Numbers

3.3 Addition and Subtraction of Rational Numbers In this section we consider addition and subtraction of both fractions and decimals. We start with addition and subtraction of fractions with the same denominator.

### Scientific Calculator

TI-30 eco RS Scientific Calculator English Basic Operations... 2 Results... 2 Basic Arithmetic... 2 Percents... 3 Fractions... 3 Powers and Roots... 4 Logarithmic Functions... 5 Angle Units... 5 DMS...

### MBA Jump Start Program

MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right