1. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific & Engineering Notation
Project Lead The Way, Inc.
Copyright 2009

2. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific & Engineering Notation
This presentation will demonstrate…
How to express numbers in scientific notation.
How to express numbers in engineering notation.
How to express numbers in SI prefix notation.
Introductory Slide / Overview of Presentation
Project Lead The Way, Inc.
Copyright 2009

3. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation
Scientific notation is a way of writing very large and very small numbers in a compact form.
A number written in scientific notation is written in the form:
a × 10b
Where: a is a number greater than 1 and less than 9.99
b is an integer
Examples:
3.24 × 105
1.435 × 10-7
3.29× 106
7.3 × 10−2
Overview and definition of scientific notation.
Project Lead The Way, Inc.
Copyright 2009

4. Writing A Number in Scientific Notation
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Writing A Number in Scientific Notation
Shift the decimal point so that there is one digit (which cannot be zero) before the decimal point.
Multiply by a power of 10, equal to the number of places the decimal point has been moved.
The power of 10 is positive if the decimal point is moved to the left and negative if the decimal point is moved to the right.
Process for writing a number in scientific notation.
Project Lead The Way, Inc.
Copyright 2009

5. Scientific Notation: Example #1
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation: Example #1
Example:
Express 5630 in scientific notation.
Pause the presentation and allow students to complete the example. The solution is on the next slide. 5
Project Lead The Way, Inc.
Copyright 2009

6. Scientific Notation: Example #1
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation: Example #1
Example:
Express 5630 in scientific notation.
Solution:
5630 =
= × 103
3 Moves
This slide includes the solution to Scientific Notation: Example #1. If you print handouts, do not print this page.
Note: Because the decimal point was moved to the left, the power of 10 is positive. 6
Project Lead The Way, Inc.
Copyright 2009

7. Scientific Notation: Example #2
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation: Example #2
Example:
Express in scientific notation.
Pause the presentation and allow students to complete the example. The solution is on the next slide. 7
Project Lead The Way, Inc.
Copyright 2009

8. Scientific Notation: Example #2
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation: Example #2
Example:
Express in Scientific Notation.
Solution:
= 6.28 × 10-4
4 Moves
This slide includes the solution to Scientific Notation: Example #2. If you print handouts, do not print this page.
Note: Because the decimal point was moved to the right, the power of 10 is negative. 8
Project Lead The Way, Inc.
Copyright 2009

9. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation
Engineering notation is similar to scientific notation. In engineering notation the powers of ten are always multiples of 3.
A number written in engineering notation is written in the form:
a × 10b
Where: a is a number greater than 1 and less than 999
b is an integer multiple of three
Examples:
71.24 × 103
4.32 × 10-6
320.49× 109
× 10−12
Overview and definition of engineering notation.
Project Lead The Way, Inc.
Copyright 2009

10. Writing A Number in Engineering Notation
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Writing A Number in Engineering Notation
Shift the decimal point in “groups of three” until the number before the decimal point is between 0 and 999.
Multiply by a power of 10 that is equal to the number of places the decimal point has been moved.
The power of 10 is positive if the decimal point is moved to the left and negative if the decimal point is moved to the right.
Process for writing a number in engineering notation.
Project Lead The Way, Inc.
Copyright 2009

11. Engineering Notation: Example #1
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation: Example #1
Example:
Express in engineering notation.
Pause the presentation and allow students to complete the example. The solution is on the next slide. 11
Project Lead The Way, Inc.
Copyright 2009

12. Engineering Notation: Example #1
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation: Example #1
Example:
Express in engineering notation.
Solution: =
= × 109
9 Moves
This slide includes the solution to Engineering Notation: Example #1. If you print handouts, do not print this page.
Note : Because the decimal point was moved to the left, the power of 10 is positive. 12
Project Lead The Way, Inc.
Copyright 2009

13. Engineering Notation: Example #2
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation: Example #2
Example:
Express in engineering notation.
Pause the presentation and allow students to complete the example. The solution is on the next slide. 13
Project Lead The Way, Inc.
Copyright 2009

14. Engineering Notation: Example #2
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation: Example #2
Example:
Express in engineering notation.
Solution: =
= × 10-6
6 Moves
This slide includes the solution to Engineering Notation: Example #2. If you print handouts, do not print this page.
Note : Because the decimal point was moved to the right, the power of 10 is negative. 14
Project Lead The Way, Inc.
Copyright 2009

15. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Prefixes
SI prefixes are a shorthand way of writing engineering notation for SI numbers.
The International System of Units (abbreviated SI from the French Système International d'Unités) is the modern form of the metric system. It is the world's most widely used system of units for science and engineering.
Overview and definition of SI Prefixes
Project Lead The Way, Inc.
Copyright 2009

16. Commonly Used SI Prefixes
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Commonly Used SI Prefixes
Value
Prefix
Symbol
1012
tera T
109
giga G
106
mega M
103
kilo k
10-3
milli m
10-6
micro 
10-9
nano n
10-12
pico p
10-15
femto f
SI Prefixes commonly used in electronics.
Project Lead The Way, Inc.
Copyright 2009

17. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Notation: Example #1
Example:
Express  using standard SI notation.
(Note:  is the Greek letter omega. In electronics, it is the symbol used for resistance.)
Pause the presentation and allow students to complete the example. The solution is on the next slide. 17
Project Lead The Way, Inc.
Copyright 2009

18. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Notation: Example #1
Example:
Express  using standard SI notation.
(Note:  is the Greek letter omega. In electronics, it is the symbol used for resistance.)
Solution:
27500  = 27.5 × 103  = 27.5 k 
This slide includes the solution to SI Notation: Example #1. If you print handouts, do not print this page. 18
Project Lead The Way, Inc.
Copyright 2009

19. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Notation: Example #2
Example:
Express Volts using standard SI notation.
Pause the presentation and allow students to complete the example. The solution is on the next slide. 19
Project Lead The Way, Inc.
Copyright 2009

20. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Notation: Example #2
Example:
Express Volts using standard SI notation.
Solution:
Volts = × 10-3 Volts = mVolts
Volts = × 10-6 Volts = Volts
This slide includes the solution to SI Notation: Example #2. If you print handouts, do not print this page. 20
Project Lead The Way, Inc.
Copyright 2009

21. Common Electronic Symbol & Units
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Common Electronic Symbol & Units
Quantity
Symbol
Unit
Current I
Ampere (A)
Voltage V
Volt (V)
Resistance R
Ohm ()
Frequency f
Hertz (Hz)
Capacitance C
Farad (F)
Inductance L
Henry (H)
Power P
Watt (W)
An abbreviated list of common electronics units and their symbols.
Project Lead The Way, Inc.
Copyright 2009