hey it's professor dave, let's talk about scientific notation and dimensional analysis humans like to count things. in the first civilizations we had to count in order to trade goods with one another. because we have 10 fingers we based our counting on a system of 10. if you count apples we can get to nine but if we add one more we put a 1 in the tens place and then start building up the units place again. there's a hundred place thousands and so forth. each time we reach the next factor of 10 we add a digit. but what if we wanna talk about a really big number like the number of molecules in this glass of water, or the number of stars in the universe it's going to get tedious very quickly to have to write numbers with dozens of digits we need a way to abbreviate very large and very small numbers that way is called scientific notation a number written in scientific notation will always consist of a single digit followed by a decimal point and then some other numbers depending on how many sig figs are in the value. that number is multiplied by 10 which is raised to an exponent. what this represents is the magnitude of the number. 10 squared means ten times ten which is a hundred so 1.42 times ten to the second is 142. we can get that by moving the decimal to the right twice ten to the sixth or one with six zeros is a million so five times ten to the sixth is 5 million we can get this by moving the decimal over six times adding zeros if we need to we can also discuss very tiny numbers this way. ten to the negative second means one over 10 squared or one 100th so 3.5 times ten to the -2 is .035. we can get this by moving the decimal two places to the left and eight times 10 to the -9 will be this number once we move the decimal nine times. this is useful because now we don't need inches and feet and miles we can just use one unit and express values in scientific notation for length we use meters for time we use seconds and so forth. now we can discuss the diameter of an atom and the distance to the nearest star in the same unit: meters just with scientific notation. we can also use unit modifiers to symbolize different magnitudes. kilo means tend to the third which is a thousand so a kilogram is a thousand grams. nano is 10 to the -9 which is one 1 billionth so a nanometer is this many meters so we can express values with a word to indicate magnitude instead a specific factor of 10. here are the different modifiers we use we can apply them to any unit and they will do the same thing to convert between units we need to do dimensional analysis let's say we have a value in meters that we want to express in nanometers. we take the value we have and we multiply by a fraction that is equal to 1. we do this because multiplying by one doesn't change the value but we multiply by a version of one that changes the way the value is expressed. we do this by putting things on the top and bottom that are equal to each other. in this case ten to the nine nanometers on the top and one meter on the bottom. these are equal because if a nanometer is a billionth of a meter then there are one billion of them in one meter so since these are equal this fraction equals 1 but the meters cancel just like an algebraic variable and now we have a value in nanometers. it's the same value we had but expressed differently. we can do this to convert between any units, just multiply by fractions that equal one until you have the value expressed in the units you want. for example how many seconds are in a year? lets use some conversion factors we know: 365 days in a year 24 hours in a day, 60 minutes in an hour sixty seconds in a minute. all the units cancel except seconds and we just multiply the numbers to get the answer these are exactly the same length of time just expressed differently. let's check comprehension thanks for watching guys. subscribe to my channel for more tutorials and as always feel free to email me