Math principle

Chapter
2
Math Principles
Section 1.1 p1

Section 1.1 p2
Math concepts are used as part of many jobs in manufacturing and
engineering. While many calculations are performed by automation tools or by
using calculators, it is important to understand concepts that are related to
mathematics in electronics.
Objectives
In this section you will learn to:
- Define counting systems and measurement systems used in electronics
- Select correct expressions of scientificnotation
- Identify measurement units used inelectronics
Section Introduction

Section 1.1 p3
Outline
This lesson has three sections: Counting and Measurement Systems, Scientific
Notation, and Units of Measurement and Conversions.
There are three primary counting systems used in electronics: The decimal
system, the binary system and the hexadecimal system.
There are four commonly used measuring systems: Systems International, Metric,
UK and US.
Video: https://www.youtube.com/watch?v=LpuPe81bc2w
Section Introduction

Section 1.1 p4
Decimal System
We use the ten digits 0-9 and calculate in factors of 10. For example, the number
529 could be represented as such:
5 hundreds
2 tens
9 ones
Define counting systems and measurement system units

Section 1.1 p5
Binary System
The Binary System of numeration is the simplest of all positional number systems.
The base of the binary system is 2, which means that only two digits - 0 and 1 -
may appear in a binary representation of any number.

Section 1.1 p6
Computers and Binary Code
This number sequence is the basis for understanding computer logic. It will appear
over-and-over.
For example, computer memory(RAM) comes in chip sizes of: 1, 2, 4, 8, 16, 32, 64,
128, and 256. There are many different ways that binary numbers are represented
at the computer's level.

Section 1.1 p7
Hexadecimal System
A hexadecimal system means counting from one to fifteen, with the sixteenth
number represented as the two digit number "10". In the hexadecimal system, the
numbers "10," "11," "12," "13," "14," "15" are symbolized as "A," "B," "C," "D," "E,"
"F"; this means the numbers ten to fifteen under the decimal system can be
characterized by onesingle digit under the hexadecimal system.

Section 1.1 p8
A comparison of counting systems:

Section 1.1 p9
Hexadecimal Color Attributes
The hexadecimal system is used for any color attribute. For example, the color
blue is expressed like this: <BODY BGCOLOR=#0000FF> The pound sign means the
following numbers represent a color

Section 1.1 p12
International System of Units (SI)

Section 1.1 p13
Metric System of Measurements

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UK (Imperial) System of Measurements

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US System of Measurements

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1. True or False: This question is an example of a binary system if true=1 and
false=0.
True
False
2. Which system represents a base 10 system?
A. Hexadecimal
B. Decimal
C. Binary
D. None of the above
Question

Section 1.1 p17
3. Which of the following systems is the most widely used in science and trade?
A. US System
B. UK System
C. Metric and SI
D. None of the above
Question

Section 1.1 p18
Scientific notation is a short-hand way of writing very large and very small
numbers.
Example: if you were measuring mass of the earth without using scientific
notation, it would look like this:
5,980,000,000,000,000,000,000,000 kilograms.
If you use scientific notation for the same measurement, it would look like this:
5.98 X 10 to the 24th Power kilograms.
This translates to 598 with 22 zeros after it.
For this number, the 24th power means that the decimal was moved to the right
24 times.
Scientific Notation Components

Section 1.1 p19
Scientific Notation Components

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1. Select the notation below that represents the correct scientific format for
the number 123,000,000,000.
A. 12.3 x 10 to the 8th power
B. .123 x 10 to the 10th power
C. 1.23 x 10 to the 11th power
D. 123 x 10 to the 12th power
2. True or False: 0.000001234 is the correct standard notation for the scientific
notation of 1.234 x 10 to the -6th power.
True
False
Question

Section 1.1 p21
1. If you were to multiply 100,000 X 10,000 using exponents, it would be
expressed in which exponent equation?
A. 10 to the 5th power X 10 to the 4th power = 100 X 10 to the 1st power
B. 10 to the 5th power X 10 to the 4th power = 10 to the 9th power
C. 10 to the 4th power X 10 to the 5th power = 10 to the 20th power
D. 10 to the 3rd power X 10 to the 5th power = 10 to the 15th power
2. True or False: 0.000001234 is the correct standard notation for the scientific
notation of 1.234 x 10 to the 6th power.
True
False
Question

Section 1.1 p23
Properties and Units
Properties are the items being measured. Units are the representation of
measurement, and the abbreviation is how the unit is commonly shown in specs,
gauges and other communication.
Example: a type of property could be land. Land is measured in acres or parcels,
which is the unit. The abbreviation on land
deeds for parcels is pcl.
Units of Measurement and Conversions

Section 1.1 p24
SI Property Units and Abbreviations
Each type of property has a unit of measurement. Each unit has an abbreviation.
There are 7 common properties used in electronics that are part of the System
International (SI) measurement system.
Roll over each bullet below with your mouse see the units of measurement and
their abbreviations and an example.
- Length
- Mass
- Time
- Electric current
- Temperature
- Light intensity
- Molecular substance

Section 1.1 p25
Additional Units
From the 7 basic units of the SI, other units were derived to measure
specific elements of physics and electricity. Roll over each bullet below
with your mouse see the SI abbreviations and units.
- Capacitance
- Frequency
- Work
- Force
- Resistance
- Pressure
- Electrical potential
- Power

Section 1.1 p26
Temperature Conversions Example
Temperature is measured in Degrees Kelvin or K, Centigrade, or C and Fahrenheit
or F.
The conversion formulas are:
K= C+273
F= 9 over 5 C+32
C= 5 over 9 times F-32

Section 1.1 p27
Practice
Match the correct properties to the corresponding SI units.
Capacitance Hertz
Force Volt
Resistance Newton
Frequency Pascal
Power Farad
Work/Energy Watt
Pressure Joule
Electrical Potent Ohm

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