[Music] good day and welcome to big bad tech i'm instructor jim pytel today's topic of discussion is engineering notation our objective is to learn to employ engineering notation in an effort to make unusually large or unusually small numbers easy to write read and most importantly conceptualize bottom line up front engineers and technicians use engineering notation and if you can't use or read numbers expressed using engineering format you can't be an engineer or technician so pay attention because i'm presuming that's what you're here for over the next several lectures i plan on performing a comprehensive review of basic math skills we'll be using during the course of this lecture series however i decided to push the discussion on engineering notation up front because it's super duper important and coincidentally the one skill most people new to the engineering game consistently struggle with most students that enroll in introductory electrical circuits classes know or at least have a passing familiarity with basic math skills like the order of operations algebraic manipulation unit conversion rounding however when someone introduces engineering notation that's when people's heads explode fair warning learning engineering notation is equivalent to learning a new language and learning a new language takes copious amounts of practice believe me you'll get plenty of practice engineering notation will be used for the remainder of this playlist and others and a solid understanding of its importance and its use is essential for success and technical career fields dominated by numbers as such i'm encouraging you to get involved with this lecture by pausing the lecture often and working out some of the illustrated example problems by yourself ideally your answer should match those of the illustrated example problem if not the illustrated example problem is there to guide you to the correct solution let us begin like i said before the goal of engineering notation is to make unusually large and usually small numbers easier to write read and most importantly conceptualize consider the unwieldiness of numbers like 560 000 volts 10 million ohms .00002 amps and point zero zero zero zero zero zero zero zero zero zero three three ferrets at first glance all these zeros blend together like a herd of zebras trying to confuse a predator and there's no way to quickly ascertain if a number is larger much larger smaller or much smaller than another additionally imagine the time you need to spend writing and reading all these zeros and not make an error engineering notation solves this dilemma by bracketing numbers into easily conceptualized levels of magnitude where numbers can be quickly compared to one another for those you versed in scientific notation as used in chemistry and other pure sciences engineering notation is a related technique but it's better how much better 10 to the third or 1000 times better allow me to demonstrate the key to engineering notation is breaking unusually large and unusually small numbers into groups of three this is a pretty natural inclination for people that use commas to separate large numbers consider the number 560 000 volts if you're like most people you'd probably put a comma right here clearly this is a pretty big number bigger than let's say 56 000 volts much bigger than 5600 volts and much much bigger than 560 volts yet at the same time it's smaller than 5 600 000 volts much smaller than 56 million volts and much much smaller than 560 million volts all of these numbers have a 5 and a 6 in them but represent startlingly different orders of magnitude if you hooked up a device intended to operate at 000 volts to a 560 volt power supply it probably wouldn't work if you hooked up that same device intended to operate at 560 000 volts to a 560 million volt supply you'd probably die for all these numbers the five and the six are the only part that actually delivers information all the zeros at the end just tell us how big or small this number is all we need is a shorthand way of expressing all these zeros that saves time and space if you think about it you've been doing this your entire life already listen to my emphatic pronunciation of our original number of interest 560 thousand i say again 560 000 the thousand at the end clearly distinguishes this from other similar sounding numbers like 560 million or just plain old 560 without any modifier at the end 560 000 is 560 times 1000 which is a one with three zeros whereas 560 million will be 560 times a million which is one with six zeros similarly 560 without any modifier at the end is 560 times one which is a one with zero zeros that's really what engineering notation is it's a modifier added to the end of a number and in front of the units that takes place of all those zeros the modifiers have funny names and abbreviations so it's probably worth your time to write them down numbers multiply by one get no modifier this is the base unit and doesn't necessitate any prefixes numbers multiplied by a thousand or one followed by three zeros get a kilo prefix which was written as a small k numbers multiplied by a million or one followed by six zeros get a mega prefix which is written as a capital m continuing in this fashion numbers multiplied by a billion or one followed by nine zeros get a giga prefix which is written as a capital g and lastly numbers multiplied by a trillion or one followed by 12 zeros get a tara prefix which is written as a capital t don't really worry about engineering prefixes for numbers greater than tara because these are the ones you're most likely going to run across zero three six nine twelve get it see the pattern one a thousand a million a billion a trillion etc these orders of magnitudes are where you normally put commas if you had to write the number out in longhand again consider our original number of interest 560 000 or 560 000 is 560 times a thousand or thousand is a one followed by three zeros or ten to the third get rid of the zeros and put a kilo or a small k in there 560 000 volts expressed using proper engineering format is 560 kilovolts where again the small k kilo prefix is equivalent to three zeros or a thousand i say again the kilo prefix means multiply the number in front of it by a thousand as a means of comparison consider the much larger number 560 million volts which is 560 times a million or a million is a one followed by six zeros or 10 to the sixth get rid of the zeros and put a mega or capital m in there 560 million volts expressed using proper engineering format is 560 mega volts or again the big m mega prefix is equivalent to six zeros i say again the mega prefix means multiply this number by a million you track it so far let's try another example consider a resistor a type of electrical component will examine greater detail in later lectures having a specified value of 10 million ohms look at where the commas go thousand million we can represent this as 10 times a million or 10 times 10 to the sixth which prefix represents six zeros or a million again we're inside the mega range so 10 million ohms is more succinctly represented as 10 mega ohms before we move on to other examples allow me to make a comment about the significance of dividing larger numbers up into groups of three if you think about the coefficient i the lead portion of the number in question that actually carries information given a maximum of three spaces we're effectively limiting the range of this coefficient to a low of one up to a maximum of less than a thousand including non-whole numbers if the coefficient is less than one you should be using the next smaller prefix if however the coefficient is greater than a thousand you should be using the next larger prefix long story short if your coefficient is greater than one and less than a thousand you're doing it right if however your coefficient is less than one or greater than a thousand you're doing it wrong additionally i'm encouraging you to think beyond the useful but clunky idea of multiplying something by a thousand a million a billion and so on i've found a far simpler way of thinking about engineering notation is moving the decimal point left or right in three-step increments think of each engineering prefix as occupying a vertical column three spaces wide consider the original number expressed in the base units of volts 560 000 volts has a decimal place right here the actual part carrying information appears to be inside the kilo column take the decimal place intended for the base unit and move it three places to the left or positive three spaces tell everyone you move the decimal place left three spaces by using a kilo prefix 560 kilovolts consider the second example express the base unit of ohms 10 million ohms has a decimal place here the actual part carrying information appears to be in the mega column take the decimal place intended for the base unit and move it six places to the left or positive six places tell everyone you move the decimal place left six spaces by using a mega prefix 10 mega ohms if you think in this fashion one can lay out any number of interest in a horizontal row and just see which vertical prefix column is the most appropriate let's try this technique on a selection of values 2200 ohms 34 500 volts and 1 million 500 000 watts look at all those zeros if we had to drag this many zeros along with us all day it'd be like carrying a 20-foot pine tree around with limbs and roots attached let's lighten our load a bit by placing these numbers in proper engineering format let's look at the first example 2 200 ohms if we overlay the number on the vertical columns associated with each engineering prefix we see it's straddling the kilo and the base unit range if we move the decimal places left three spaces it gives us a coefficient of 2.2 i.e something one or greater and less than a thousand a three decimal place jump left is a kilo so this number might be more compactly expressed as 2.2 kilo ohms let's look at the next example 34 500 volts again if we overlay the number on the vertical columns associated with each engineering prefix we see it straddling the kilo and base unit range if we move the decimal place left three spaces it gives us a coefficient of 34.5 by something one or greater and less than a thousand a three decimal place jump left is a kilo so this number might be more compactly expressed as 34.5 kilovolts let's look at the final example one million five hundred thousand watts again if we overlay the number of the vertical columns associated with each engineering prefix we see it's straddling the mega and kilo range if we move the decimal place left six spaces it gives us a coefficient of one point five at a something one or greater less than a thousand a six decimal point jump left is a mega so this might be more compactly expresses 1.5 megawatts too easy right here's another set of examples this time you're on your own so if you place these unwieldy numbers in proper engineering format where proper engineering format uses coefficient of one or greater and less than a thousand and our appropriate prefix representing its magnitude don't worry so much about what each unit represents right now we'll examine the units and quantities they represent in later lectures by all means pause the lecture and try these examples by yourself now do not just sit there with a dumb look on your face and wait for me to give you the answers do what i'm telling you to do pause the lecture and try these example problems by yourself if you're tracking you should have obtained the following values our first entry is better expressed as 2.45 megawatts our next entry is properly expressed as 9.1 giga ohms the third one doesn't necessitate engineering prefixes because it's already appropriately expressed in the base unit so 208 volts is 208 volts our next entry is more compactly expressed as 3.6 terajoules and finally our last entry is better expresses two kilometers all right if that's that went well you're most likely getting a tentative hold on placing large numbers in proper engineering format where again proper engineering format uses some coefficient one or greater and less than a thousand and a prefix in front of the unit where each prefix represents a shift in three-step increments 3 6 9 12 and so on let's now explore an additional utility of engineering prefixes as i mentioned previously engineering prefixes aren't limited to expressing only unusually large numbers in a more compact and usable form they can also be used to make working with unusually small numbers easier and dare i say more enjoyable i'm going to demonstrate but first a minor detour through mathlan might be necessary the mathematically inclined among you may recall the significance of negative exponentiation mathematically uninclined may not in this spirit let us review negative exponents by way of a series of illustrated examples consider the expression 2 to the negative 1. this means take 1 over 2 and raise 2 to the first power 2 to the first power is 2 so 1 over 2 is 0.5 similarly consider the expression 2 raised to the negative 2 this means take 1 over 2 and raise 2 to the second power 2 to the second power is 4 and 1 over 4 is 0.25 lastly consider the expression 2 raised to the negative 3. this means take 1 over 2 and raise 2 to the third power 2 to the third power is 8 and 1 over 8 is 0.125 you'll note increasing the magnitude of the negative exponent negative 1 to negative 2 negative 2 to negative 3 and so on correspondingly decreases the result 0.5 down to 0.25 down to 0.125 and so on this concludes this brief review of negative exponents returning the task at hand engineering prefixes concern themselves solely with powers of 10 and three-step shifts positive powers of 10 like 10 raised to the third 10 raised to the 6 10 raised to the 9th and so on are associated with leftward shifts associated with ever greater larger numbers whereas negative powers of 10 like 10 to the negative third 10 to the negative 6 and 10 to the negative 9th and so on are associated with rightward shifts associated with ever smaller small numbers consider the expression 10 raised to the negative third this means take 1 over 10 and raise 10 to the third power ten to the third power is a thousand one over a thousand or one thousandth in decimal form is point zero zero one similarly consider the expression ten to the negative six this means take one over ten and raise ten to the sixth power where 10 to the sixth is a million one over a million or one millionth in decimal format is point zero zero zero zero zero one consider the expression ten raised to the negative ninth this means take 1 over 10 and raise 10 to the ninth power 10 to the ninth is a billion one over a billion or one billionth in decimal format is point zero zero zero zero zero zero zero zero one lastly consider the expression 10 raised to the negative 12 this means take 1 over 10 and raise 10 to the 12th power where 10 to the 12th is a trillion one over a trillion or one trillionth in decimal format is point zero zero zero zero zero zero zero zero zero zero zero one you'll ultimately realize these negative powers of ten are in effect multipliers that make a given coefficient smaller and can be used to express extremely small numbers in a combat usable fashion quite like positive powers of 10 negative powers of 10 also have their own associated engineering prefixes numbers multiplied by a thousandth or .001 get a milli prefix which is written as a small m numbers multiplied by a millionth or .0001 get a micro prefix which is written as a funny looking u with a long tail lacking the proper cube of this symbol are more appropriate lacking the wheel and motivation to look up the proper shortcut for this strange symbol you'll often see micro written as a regular lowercase u continuing in this fashion numbers multiply by a billionth or zero zero .00001 get a nano prefix which is written as a small n and lastly numbers multiplied by a trillionth or point zero zero zero zero zero zero zero zero zero zero zero one get a picot prefix which is written as a small p let's combine this new set of prefixes associated with small numbers with an earlier set associated with large numbers i now present to you the set of the most commonly used engineering prefixes covering the spectrum from the unimaginably large to the inconceivably small a trillion to a trillionth 10 to the 12th terra or big t 10 to the ninth giga or big g 10 to the sixth mega or big m 10 to the third kilo or lower case k the base unit necessitating no prefix now it's mirror image 10 to the negative 3 milli or lower case m 10 to the negative 6 micro or u with a funny tail 10 to the negative 9th nano or lower case n and finally 10 to the negative 12 pico or lowercase p chances are you'll never have the occasion to use anything above or below the ranges are presented here my sincere advice is to take the time necessary to commit this relationship to memory i say again my sincere advice is to take the time necessary to commit this relationship to memory because one day someone's going to take it away just kidding i bet you freaked out there don't worry i'll just keep this cheat sheet on the screen for a little bit so you can copy it down in your notebook some of the advice i issued earlier about the upper range of engineering prefixes i found a far simpler way of thinking about engineering notation at the smaller end or for that matter either end is to simply move the decimal point left or right in three-step increments as required each engineering prefix gets three spaces when expressing a number in the base unit the decimal place is here the next larger prefix to the left is kilo the next larger prefix to the left is mega next larger prefix to the left is giga next larger prefix to the left is terra our last set of example problems dealt with these larger numbers smaller numbers are similar only they're on the right starting the base unit the decimal place is here the next smaller prefix to the right is milli the next smaller prefix to the right is micro the next small prefix to the right is nano the next smaller prefix to the right is pico every prefix gets three spaces as previously if you think in this fashion one can lay out any number of interest in a horizontal row and you see which vertical prefix common is the most appropriate for example consider the number .00002 amps i know you don't normally see them in smaller numbers but where would you put a comma in such a long string of numbers chances are right here again think in groups of three you know the very far right side isn't a group of three but rather only two feel free to add another zero to make it a group of three because there's an endless string of invisible zeros behind every number and you can add or not add as many as you like our number of interest is now point zero zero zero zero two zero divided into two groups of three as previously if we overlay the number on the vertical columns associated with each engineering prefix we see it's inside the micro range if we move the decimal place right six spaces or negative six spaces if you will it gives us a coefficient of 20. i something one or greater and less than a thousand a six decimal point jump right is a micro so this number might be more compactly expressed as 20 microamps an amp by the way is unit current flow i.e a quantity of charges passing by a point in space per unit time we'll examine current and other electrical properties in later lectures similarly consider the extremely small number .00000 0 3 3 fair adds where a fair ad is a quantity of charges stored per volt associated with the type of electrical component called the capacitor we'll examine capacitors in later lectures can we use engineer prefixes to tame this wild herd of zeros and represent this unwieldy measurement in a more docile and manageable form yes yes we can allow me to demonstrate break this tangled mass of zeros into four groups of threes overlay the vertical columns associated with each engineering prefix and see where it most comfortably resides we see it's inside the pico range if we move the decimal point right 12 spaces or negative 12 spaces if you will it gives us a coefficient of i.e something one or greater and less than a thousand a 12 decimal point jump right is a picot so this number might be more compactly expressed is 33 pico ferrets want to give this a go yourself be my guest here's a couple of extremely small numbers see if you can use your new understanding of engineer prefixes to put them in the proper engineering format again don't worry so much about what each unit represents right now we'll examine the units and quantities they represent in later lectures by all means pause the lecture and try these examples by yourself if you're tracking you should obtain the following values our first entry point one two zero henries is better expressed as 120 millihenries our next entry .0002 coulombs is more appropriately represented as 2.2 micro coulombs our next entry .03 amps is better represented as 30 milliamps and lastly point zero zero zero zero zero zero zero one five farads is more compactly represented as fifteen nanofarads all right if this last part went well you're most likely now getting a tentative hold on placing small numbers in proper engineering format let's finish up this lecture with a set of illustrated examples featuring both small and large numbers if you can survive this meeting engagement with your sense of dignity intact you're tracking and you can move on to the next lecture if not you are not tracking and you need to rewind or revisit the contents of this lecture as i mentioned previously engineers and technicians use engineering prefixes and if you can't use engineering prefixes you can't be an engineer or technician learn this technique now and put it behind you quick because i've got a bunch of other stuff coming your way real soon all right see if you can place these unwieldy numbers in proper engineering format where proper engineering format again uses a coefficient one or greater and less than a thousand and a prefix representing a magnitude feel free to use the prefixes overlay if that helps you out by all means pause the lecture try these examples by yourself if you're tracking you should have obtained the following values for our first example four million two hundred thousand hertz is more appropriately expressed as four point two megahertz our next entry point zero three four five amps is more appropriately represented as 34.5 milliamps our next example point zero zero zero zero four farads is more appropriately represented as 40 microfarads our next example 12 volts is already improper engineering format so 12 volts is most appropriately expressed as 12 volts our next example 10 billion watts is best expressed as 10 gigawatts our next example five thousand seven hundred watt hours is more appropriately expressed as five point seven kilowatt hours our next entry point zero zero zero zero zero zero zero zero zero six 630 fair ads is more compactly represented as 630 picofarads our next entry 34 trillion joules is more appropriately represented as 34 tera joules lastly point zero zero zero zero zero zero zero zero one meters is more appropriately represented as one nanometer all right if that last part went well i hereby proclaim you marginally proficient in engineering prefixes if i was a lesser instructor i'm concerned about your future we'd probably call it quits and let you go outside to play but that's not why you're here is it you're here for my own special brand of cold hard discipline am i right let's try one more exercise before we bring this lecture to a close consider the selection of entries each measurement of the fictitious unit of surprise specified of the units of zoinks abbreviated with a capital z or surprise of one mega zoink is sufficient to stampede a herd of water buffalo versus surprise of only one millizoink is barely enough surprise to register notice like say seeing water buffalo next to a body of water i'm asking you to do two tasks one place these entries in proper engineering format and two arrange them in a sequence largest to smallest again i'm asking you to do two tasks one place these entries in proper engineering format and two arrange them in sequence largest to smallest by all means pause the lecture and try this yourself if you're tracking you should obtain the following values our first entry 33 000 zoinks is better expressed as 33 kilozoinks our next entry 23 million 800 000 zoinks is better expressed as 23.8 megazoix our next entry 24 zoinks is already in proper engineering format so 24 zoinks improper engineering format is 24 zoinks our next entry 0.196 zoinks is more compactly expressed as 196 millizoinks our next entry 8 billion 700 million zoinks is more usably expressed as 8.7 gigazoics our next entry 0.047 zoinks is more appropriately expressed as 47 millisonics something a thousand times smaller or .0047 zoinks is more appropriately expressed as 47 microzoinks this large value of 2 trillion 840 billion zoinks is better expressed as 2.84 pterozoics lastly this extremely small value of 0.000022 is more efficiently expressed as 22 picozoinks lastly we've been asked to arrange these entries in a sequence this is where engineer prefixes truly show their worth for a quick discernment of magnitude one can simply ignore the coefficient and look at the prefix for those entries the same prefix that's the only time you have to compare the magnitudes if you're tracking your sequence should have looked something like this 2.84 pterozoics is the largest entry followed by 8.7 gigazoics 23.8 megazoinks 33 kilozoinks 24 zoinks 196 milliseconds 47 millizoinks 47 microzoinks and finally the smallest entry 22 picozoinks there you have it all of our original unwieldy numbers have now been placed in engineering format and arranged in a proper sequence befitting their magnitude i'm asking to consider two major advantages of engineering prefixes one the numbers expressed in engineering format are far more compact and far easier to write and read than the original numbers there's no tangled string of confusing zeros in the coefficient being the only part of the original number that actually delivers information is readily apparent two and this is important magnitude is easily discernible ignore the coefficient a tara is 1 000 times larger than a giga a giga is 1 000 times larger than a mega and so on only in cases of equal prefixes as in the case of 196 millisonks and 47 millizoinks does one actually have to go to the trouble of comparing numbers all right that about wraps up this introductory discussion on engineering notation stay tuned for upcoming lectures featuring engineering notation on the scientific calculator and conversions between different engineering prefixes in conclusion this lecture took a look at engineering notation we learned engineering prefixes make unusually large or unusually small numbers easier to read write and most importantly conceptualize additionally we learned engineering prefixes can be used to quickly ascertain whether a number is greater much greater smaller or much smaller than another remember to review this material as often as you need to really drive it home imagine how well lab will go if you know what you're doing thank you very much for your attention and interest we'll see you again during the next lecture of remember to tell your lazy lab partner about this resource be sure to check out the big bad tech channel for additional resources and updates [Music] you