# PmP612s Lecture Notes - Lecture 5: Web Conferencing, Elementary Arithmetic, Therm

16 pages30 viewsFall 2015

Department

Human ResourcesCourse Code

PmP612sProfessor

NyguynLecture

5Business Energy Professional – Math Supplement

As a supplement to the Business Energy Professional course, we routinely hear from

seminar or webinar attendees that they wish there was an overview of math skills

needed for the course. This handout contains an overview of the math skills needed for

simplifying expressions, converting units, utilizing calculators, and solving equations

typically found in the Business Energy Professional Course. Please recognize that

anything you do prior to the course in reviewing this material will substantially increase

what you learn during the seminar or webinar and will also service those very well as

they prepare for the certification exam. This handout is broken into the following

sections:

Order of Operations / Hierarchy

Calculators

Expressions

Conversion Factors for Unit Conversions

Unit Conversions

Equations

While this handout is a short refresher of several mathematical operations, the

Association of Energy Engineers does offer a very extensive pre-course titled “The

Basics of Energy Management”. This online self study course is not required for the

Business Energy Professional course or its certification. Some individuals may find the

online course worth their while as a review course. The Basics of Energy Management

self study seminar outline is as follows.

Basics of Energy Management Seminar Outline

Preface -- Goals and Purpose of This Self-Paced Seminar

Chapter 1 Introduction to Energy Management

Chapter 2 What is Energy and National Energy Use

Chapter 3 Basic Arithmetic and Calculator Skills

Chapter 4 Basic Algebra and Analytical Skills

Chapter 5 Energy Units and Energy Conversions

Chapter 6 Understanding Electrical Systems and Electrical Rates

Chapter 7 Economic Analysis and Economic Decisions

Chapter 8 Basic Technologies, Terminology and Units for Equipment End Use

Categories - Lighting, Motors, Air Conditioning, and Boilers

Order of Operations / Hierarchy:

The order of operations or hierarchy is the order in which a mathematical expression or

equation should be conducted. The hierarchy of operations is as follows:

1. Operations inside grouping symbols

2. Exponents

3. Multiplication and/or Division in the order of left to right

4. Addition and/or subtraction in the order of left to right

Examples:

1. 7 + 3 x 4 + 6

For this expression, the first operation must be the 3 x 4

7 + 12 + 6

The next order would be the addition, in order from left to right

25

2.

For this expression, the first operation must be the exponents

6 x 49 x 5 + 14 x .81

The next order would be the multiplication, in order from left to right

1,470 + 11.34

The next order would be the addition, in order from left to right

1,481.34

3.

For this expression, the first operation must be the exponents (we must

reduce these to fully do the operation within the grouping symbol)

133 x (.0036 + .125 x 420) + 1,728

The next order would be the multiplication within the grouping symbol

133 x (.0036 + 52.5) + 1,728

The next order would be the addition within the grouping symbol

133 x (52.5036) + 1,728

The next order would be the multiplication

6,982.9788 + 1,728

The next order would be the addition

8,710.9788

4.

For this expression, the first operation must be the operations within the

grouping symbols. For the first grouping symbol, multiplication in the order

from left to right; the second grouping symbols is addition and subtraction

in order from left to right; the third grouping symbol is the performance of

the division.

The next order would be the exponents

1,786 + 2,401{48} + .5120

The next order would be the multiplication

1,786 + 115,248 + .5120

The next order would be addition, in order from left to right

117,034.512

Important Note: Business calculators are programmed to do the order of

operations in the order that you enter them, ie – it ignores hierarchy. Whereas a

scientific calculator knows hierarchy and when posed with entering numbers, it

will perform the operations following the order of operations above.

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