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

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

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

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

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

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 = 5630.0 = 5.630 × 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

Scientific Notation: Example #2 Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter Scientific Notation: Example #2 Example: Express 0.000628 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

Scientific Notation: Example #2 Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter Scientific Notation: Example #2 Example: Express 0.000628 in Scientific Notation. Solution: 0.000628 = 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

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× 109 123.452 × 10−12 Overview and definition of engineering notation. Project Lead The Way, Inc. Copyright 2009

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

Engineering Notation: Example #1 Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter Engineering Notation: Example #1 Example: Express 16346000000 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

Engineering Notation: Example #1 Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter Engineering Notation: Example #1 Example: Express 16346000000 in engineering notation. Solution: 16346000000 = 16346000000.0 = 16.346 × 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

Engineering Notation: Example #2 Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter Engineering Notation: Example #2 Example: Express 0.0003486 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

Engineering Notation: Example #2 Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter Engineering Notation: Example #2 Example: Express 0.0003486 in engineering notation. Solution: 0.0003486 = 0.0003486 = 348.6 × 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

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

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

Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter SI Notation: Example #1 Example: Express 27500  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

Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter SI Notation: Example #1 Example: Express 27500  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

Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter SI Notation: Example #2 Example: Express 0.000568 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

Scientific & Engineering Notation Digital Electronics TM 1.1 Foundations and The Board Game Counter SI Notation: Example #2 Example: Express 0.000568 Volts using standard SI notation. Solution: 0.000568 Volts = 0.568 × 10-3 Volts = 0.568 mVolts 0.000568 Volts = 568.0 × 10-6 Volts = 568.0 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

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