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Chapter 2 Prefixes, Units and Unit Conversion Quick review on exponents 103 = 10x10x10 = 1000 10 x 3 3 x 103 = 3x10x10x10 = 3000 24 = 2x2x2x2=16 106 = 10x10x10x10x10x10 = 1,000,000 10-3 = 1/(103) = 1/1000 = .001 10-6 = 1/(106) = 1/1000,000 = .000001 5 x 10-6 = 5 x 1/(106) = 5x.000001 = .000005 Scientific Units Parameter Length Mass Time Unit Meter [m] Kilogram [kg] Second [s] For Electronics Voltage Volt [V] Current Amp [A] Ohm [Ω] Resistance Other Units Prefixes How many meters are there in a kilometer? ◦ 1000 How many milliseconds are there in a second? ◦ 1000 How many bytes are there in a Gigabyte? ◦ 1,000,000,000 Prefixes (cont.) Kilo, milli, and Giga are all called prefixes. Can you guess why they call them prefixes? Because they come before the unit such as millisecond. Prefixes are used to represent how much of the particular unit is being represented Prefixes we’ll use in Elec50A Prefix Abbrev. Example What it means Scientific Notation Giga G Gm x1,000,000,000 Mega M MV x1,000,000 Kilo k kA x1,000 Unit Base - S x1 Milli m mg x.001 Micro Or u uΩ x.000001 Nano n ns x.000000001 Pico p pA x.000000000001 x109 x106 x103 x100 x10-3 x10-6 x10-9 x10-12 In your book they show other prefixes we won’t use much if at all. Quick Prefix Quiz How seconds are there in a Gs? ◦ 1 billion How many volts in a mV? ◦ .001 How many mV in a volt? ◦ 1000 How many amps in a kiloAmp (kA)? ◦ 1000 Quick Prefix Quiz (cont.) How small is a nA ◦ 1 billionth or .000000001 A or 10-9 How small is a uΩ? ◦ 1 millionth or .000001Ω or 10-6 How big is a pV? ◦ 1 trillionth of a volt or 10-12 V 3 ways to write a number 1 million volts 1 thousandth of an amp 1 millionth of an ohm 1 billion grams 5 thousand meters 1 second Regular Way Using Prefixes Scientific Notation 1,000,000 V .001 A .000001 Ω 1MV 1mA 1uΩ 1x106 V 1x10-3 A 1x10-6 Ω 1,000,000,000 g 5000 m 1s 1Gg 5km 1s 1x109 g 5x103 m 1x100 s Notice that the prefixes take place of the scientific notation and everything else stays the same. Meaning – k = x103 Write the following in scientific notation: 3mV 18kV 43ms 2.1GA 30uA 57ps 3x10-3V 18x103V 43x10-3s 2.1x109A 30x10-6A 57x10-12s Write the following using prefixes 483x10-3A 32x106V 2x10-9A 3.4x10-12s .350x103Ω 42x10-6V 483mA 32MV 2nA 3.4ps .350kΩ 42uV Notice “m” replaced all of “x10-3” and everything else stayed the same This can be simplified to just 350 Ω More practice problems Converting regular numbers to scientific notation. Convert 4578 to scientific notation Convert .00009 to scientific notation Convert 4.56 to scientific notation What does 6.4 x 10^0 = ? 4.578 x 103 9x10-5 4.56x100 6.4 x 1 = 6.4 Notice in the above example 9x10-5 cannot be converted to a prefix very easily because there is no prefix for -5. So it is useful to convert this number to one that does have a prefix. 9x10-5 = .00009 = .000090 = 90 x 10-6 = 90u What we just did was convert scientific notation to engineering notation!!! (Go ahead and write home) So what is the difference between scientific notation and engineering notation? In scientific notation there is always only one digit or number in front of the decimal and everything else is behind the decimal. ◦ Ex: 9.54 x 10-5 In Engineering notation the exponent is always a multiple of 3. ◦ Ex: 95.4 x 10-6 ◦ Notice -6 is a multiple of 3 Notice all prefixes are multiples of 3 Prefix Abbrev. Example What it means Scientific Notation Giga G Gm x1,000,000,000 Mega M MV x1,000,000 Kilo k kA x1,000 Unit Base - S x1 Milli m mg x.001 Micro Or u uΩ x.000001 Nano n ns x.000000001 Pico p pA x.000000000001 x109 x106 x103 x100 x10-3 x10-6 x10-9 x10-12 We will be using engineering notation for electronics courses because it is useful in converting to prefixes. Convert the following to engineering notation and then to its corresponding prefix -6A = 430uA = 430 x 10 .00043A = .23V = 230x10-3V = 230mV 23x10-2V 6s = 670Ms 7 = 670000000s = 670x10 67x10 s -9s = 7.83nm = 7.83x10 .00000783m Random Video of the Day! Get out your Calulators First put your calculator in Engineering Notation ◦ ◦ ◦ ◦ ◦ ◦ ◦ Press 2nd F Press SET UP Press 1 for FSE (Fixed Scientific Engineering Press 2 for Engineering Notation Enter 9 so it shows the most amount of precision It says ENG on the left side of the screen now. If you ever want your calculator to show normal looking numbers as answers again, you’ll have to go through this process and press 0 for fixed numbers at the last step. Enter 567000 and press =. Notice it automatically put it into Engineering Notation. It shows 567E3 E is an abbreviated way of saying “x10^” 567E3 = 567 x103 Now press .0000004 and press enter You may need to press the Change button to convert it from a fraction It shows 400E-9. Convert this to a prefix 400n!!!! Look on Page 21 of your book Throughout the text book, anytime we will encounter a new feature using the calculator, it will tell you the buttons to press to perform the particular operation. Convert to a prefix using calculator .000056V 5430000A 4300Ω .00076s = 56uV = 5.43MA = 4.3kΩ = 760us Using a Calculator for this stuff 3 ways to enter these numbers Entering 5.4x103 1. Just enter 5400 2. 5.4x 10x 3 3. 5.4 EXP 3 EXP is the same thing as “x10^” Sometimes 5.4x103 can be expressed as 5.4E3. This is the same thing as 5.4 EXP 3 Converting between units Many times it is useful to convert from one prefix to another. ie: uA to nA Convert 43uA to nA ◦ 43uA = 43000nA To do this we will use 2 rules. WRITE THESE DOWN! If you are going from a larger exponent to a smaller exponent, then you move the decimal to the right If you are going from a smaller exponent to a larger exponent, then you move the decimal to the left - If you are going from a larger exponent to a smaller exponent, then you move the decimal to the right. - If you are going from a smaller exponent to a larger exponent, then you move the decimal to the left 43 Convert 43 mV into _______uV .043V 43.uV = 43uV .014 Convert 14kV into ________MV Convert 72GV into _______nV 72,000,000,000,000,000,000V - If you are going from a larger exponent to a smaller exponent, then you move the decimal to the right. - If you are going from a smaller exponent to a larger exponent, then you move the decimal to the left Now convert to Engineering Notation 10 1.5 1.2 5100 0.04 1 1500 .15 .25 3700 10x103A 1.5x106Ω 1.2x103Hz 5100 x10-6A 0.04x10-3A 1x103W 1500x10-12F .15x103V .25x106W 3700x103Ω Using the table.You have this as a handout Convert 1 microsecond into ________seconds .000001 2.8345 Convert 2834.5 nanoseconds into ________microseconds .0004 Convert .4 milliohms into __________ ohms Explaining Handout – This handout may be used on tests, but no writing may be on it. Handout Units Worksheet Lets do together 1, 2, 10, 11, 17, 22 Go ahead and finish the rest of the worksheet on your own. If you don’t finish it in class it is homework. Its due on Monday