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# Exponents and powers of 10 patterns

CCSS.Math:

## Video transcript

we are asked what is 10 to the 5th power equivalent to well 10 to the 5th power is the same thing as taking a 1 and multiplying it by 10 five times let's do that so that's 3 4 & 5 so it's 1 times 10 times 10 times 10 times 10 times 10 notice 1 2 3 4 5 and what's this going to be well 1 times 10 is 10 10 times 10 is 100 100 times 10 is 1,000 1000 times 10 is 10,000 10,000 times 10 is 100,000 so this is going to be 100 100,000 now you might have noticed every time we multiply it by 10 we're adding another zero to the product so if we're multiplying by 10 five times we're going to add five zeros to the product so this is good little ego a it's literally going to be 1 1 followed by followed by 5 zeroes 1 2 3 4 5 so 10 to the 5th is the same thing as 100,000 let's do another one that is on a similar topic how many zeros does the product 67 times 10 to the fifth have well there's a bunch of ways of thinking about that 67 67 times 10 to the fifth is the exact same thing this is equivalent to you could view this as 67 times and we could use the last exam exact logic that we just saw in the previous problem so 67 times 1 times 10 times 10 times 10 times 10 times 10 and we already figured out exactly what this is if you have 1 multiplied by 10 5 times this right over here is going to be 1 followed by 5 zeroes 1 2 3 4 5 so or it's going to be a hundred thousand so there's a couple of ways to think about it if you're looking at just this product right over here you could say well 67 times 1 is just going to be 67 and then every time you multiply it by 10 you're going to add another 0 so you could say well this is just going to be 67 and we're going to be multiplying by 10 five times so we're going to add five zeros here one two three four five and so this would come to six million seven hundred thousand another way you could think about it this is the same thing as sixty seven times 100,000 so it's going to be sixty seven and then we have five zeros here so once again one two three four five you get the exact same value let's do another one how many zeros is the quotient five million seven hundred thousand divided by ten to the third power half well ten to the third power we already know two n to the third power that's the same thing as 1 times 10 times 10 times 10 which is the same thing as 1000 and so if we're dividing by that that's the same thing so another way of writing this expression right over here so five million seven hundred thousand divided by divided by 10 to the third is the same thing is the same thing as I could write it this way five million seven hundred thousand divided by ten times ten times ten we could put a 1 out here but this won't really change the value which is equivalent to five million seven hundred thousand divided by 1000 and either way you think about it every time you divide by ten you're going to eliminate one of these zeros so if you divide by 10 three times if you divide by ten once you're going to eliminate a zero divided by ten again you're going to eliminate another zero divided by ten again you're going to eliminate another zero you're going to be left with five thousand seven hundred another way of thinking about it is well if I'm dividing by something that has three zeros I'm going to eliminate three zero so if I eliminate three zeros I eliminate three zeros I am left with five thousand seven hundred now just to be clear I could only do this because this was one thousand if this was like three thousand or something I could I could think of this as three times a thousand and then I could only cancel out the one thousand with these zeros but the three I would then have to divide separately but only because I'm straight-up dividing by a thousand I'm dividing by a power of 10 I have three zeros here I can cancel it out with three zeros there let's do another one there are ask you a few and these are the type of exact questions that you might see in the exercise when 72.1 is multiplied by 10 to the third the decimal point moves blank places to the blank and in the exercise you might see a drop down here so remember if you're multiplying by a and this is a this is a essentially 10 to the 3rd you're multiplying by a thousand you're going to get a larger number you're not you know you're not going to get a smaller number and so every time you multiply by 10 your decimal point is going to move to the right because you're getting larger so we're going to move the decimal point so 72.1 if we multiplied it by 10 once then we would move the decimal point over 1 so we get 721 which makes sense 72 times 10 is 720 72 point one times 10 should be 721 but if we want to multiply it by 10 three times we're going to move the decimal place over not just once but twice and three times and you say wait wait how can I move it over there's nothing here well you throw a zero in there and so you're going to get it's going to be equal to so it's going to be equal to 70 2,100 now they're not asking us that they're just asking how we would do it and we saw the decimal point moves three places to the right and the big key here's you're going to get a larger number when you multiply by 10 three times or multiply by a thousand let's do this one when 56 is divided by 10 to the third the decimal point moves blank places to the blank well dividing by 10 to the third is the same thing as dividing by 10 three times and every time you divide by 10 it's going to become a smaller number so 56 you might say where is the decimal point well there's implicitly a decimal point right over there you divide by 10 1 so you're going to get a smaller number 56 is going to become 5 in something so it's going to become literally five point six divided by 10 again it's going to become 0.5 6 divided by 10 again you're like wait if I keep moving the decimal place again to the left where where is what am i moving it to the left off well you can throw a zero right over here and so if you move the decimal point three places to the left three places to the left you are left with point zero five six and you might want to put a zero out here just for for clarity but what we did here is we moved the decimal point three places to the left in this situation we got a smaller value