in this lesson i want to give you a basic introduction into scientific notation scientific notation is a useful way to represent very large numbers or very small numbers so let's say if we have the number forty five thousand how can we express this number in scientific notation now you want to move the decimal in between the first two numbers that is between the four and five so i'm going to move it four units to the left one two three four so forty five thousand is equal to four point five times ten to the four now it's important to understand that if this number is positive it's associated with a very large number if this is a negative exponent it will be associated with a very small number a number between 0 and 1. so let's work on some more examples try these two examples actually maybe more than two let's say thirty seven fifty five hundred eighty thousand seventy two million and let's say 9.3 billion go ahead and convert these numbers into scientific notation feel free to pause the video so let's start with this one i'm gonna put the decimal between a three and a seven so this is one two three since i moved it three spaces to the left this is going to be 3.75 times 10 to the third power and that's pretty straightforward now let's move on to the next one so i want the decimal point to be between the 5 and the 8 so i'm going to move it 1 2 3 4 five units to the left so therefore this is going to be 5.8 times 10 to the 5. now for the next example i want it to be between a 7 and a 2. so this is going to be this is 3 6 and then 7. so i move this 7 space to the left so it's going to be 7.2 times 10 to the 7 and that's it for that one now for the last one i'm going to start here 3 6 9 units to the left so this is going to be 9.3 times 10 to the ninth power and that's a simple way to express very large numbers using scientific notation now what about some small numbers for example 0.0023 we still want the decimal to be between the two and a three but this time i'm going to move it to the right as opposed to the left so i need to move it three spaces to the right so therefore this is going to be 2.3 times 10 to the negative 3. now keep in mind a negative exponent will always be associated with very small numbers a positive exponent will be associated with very large numbers here's some more examples that you can try so go ahead and try those examples so this is three four units so this is going to be 7.6 times 10 to the negative 4. so anytime you have these decimal values it's going to have a negative exponent associated with the scientific notation number so for this one i've got to move it two units to the right and so that's going to be four point nine times ten to the minus two now for the third example this is three six seven actually not that far i needed to be between the first two numbers so three and six so this is going to be five point four one times ten to the negative six this is 3 6 9 and then 10 units to the right so this is going to equal 8.35 times 10 to the negative 10. and so now you know how to convert a number in decimal notation or standard notation into scientific notation now let's switch it up a bit let's work on converting a number from scientific notation standard notation so let's say if we have 2.4 times 10 to the 2 what is this equal to now keep in mind that we said that if we have a positive exponent it will be associated with a larger number so we need to increase the value of 2.4 so should we move the decimal to the right or to the left to increase the value we need to move it to the right so we have the number 2.4 and let's add some zeros to it so we're going to move it two units to the right so therefore this is going to change to 240 and that's the answer now if you think about what this expression means 10 squared that's 10 times 10 which is 100 so this really means 2.4 times 100 which is 240. and so you could see it that way if you want to as well let's try this example 3.56 times 10 to the third power so we need to move the decimal 3 units to the right so this is one two three so we need to add another zero so therefore this is going to be three thousand five hundred and sixty so ten to the third means that well ten times ten times ten that's a thousand with three zeros and three point five six times a thousand is thirty five sixty go ahead and try these two examples four point two seven times ten to the five and also three point nine six times ten to the seven so let's start with this one four point two seven let's move the decimal point five units to the right so that's two three four five so we need to add three zeros so this is going to be four two seven zero zero zero or four hundred twenty seven thousand ten to the fifth is basically a hundred thousand so a hundred thousand times uh four point two seven that's four hundred twenty seven thousand now let's try this one so we have three point nine six and we need to move the decimal point seven units to the right so one two three four five six seven and so we need to add five zeros so the answer is going to be three nine six zero zero zero zero zero so that's 39 million six hundred thousand now let's work on some examples with negative exponents so a negative exponent is going to be associated with a small number so this time we need to move to the left so let's move three spaces to the left one two three so we need to add two zeros so therefore this is going to be point zero zero three seven let's try this example four point one six times ten to the negative five so we need to move five spaces to the left one two three four five so this is going to be point zero zero zero zero four one six now let's work on a mixed review go ahead and convert the following numbers into scientific notation let's see if you remember how to do this so the first one is a small number so it's going to be associated with a negative exponent we need to move the decimal point between the seven and the three between the first two non-zero numbers so since we move it three units to the right it's going to be 7.35 times ten to the negative three now let's move on to the next example we have a large number and we need to put the decimal between the first two non-zero numbers between the three and six so we're going to move it three four five spaces to the left so this is going to be 3.64 times 10 to the positive 5 since we have a large number now the next example is a small number and we only need to move it two spaces to the left so this is going to be 1.5 times 10 to the minus 2. and for the last example we have a large number and we're going to move it three spaces to the left so this is going to be 2.8 times 10 to the 3. so keep that in mind anytime you have positive exponents it always will be associated with large numbers and small numbers that are between 0 and 1 are associated with negative exponents that will help you to determine which direction you need to move the decimal point so let's try some more examples 1.8 times 10 to the minus 3 four point one times ten to the two one point two times ten to the negative five and two point seven times ten to the four so let's convert this to standard notation so let's start with the first example should we move the decimal point to the left or to the right this is particularly useful if you need to convert it from scientific notation to standard form since we have a negative exponent we need a small number so we got to move to the left one two three so we're going to fill these spaces with zeros so therefore this is going to be .0018 now for the next example we have a positive exponent so that's associated with a large number therefore we need to move the decimal point to the right two spaces so we're going to add a zero here therefore that's going to be 410. now for the next example we need to move it to the left one two three four five so therefore that's going to be point zero zero zero zero one two and for the last one we need to move it to the right so one two three four and so that's going to be 27 000 so hopefully this video gave you a good introduction into scientific notation and how to convert back and forth into standard notation so thanks again for watching you