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# Orders of magnitude exercise example 2

## Video transcript

let's do a few more examples from the orders of magnitude exercise earth is approximately 1 times 10 to the seventh meters in diameter which of the following could be Earth's diameter so this is just an approximation it's an estimate and they're saying which of these if I wanted to estimate it would be close sort would be 1 times 10 to the seventh and the key here does realize that 1 times 10 to the seventh one times 10 to the seventh is the same thing as one followed by seven zeroes one two three four five six seven we put some commas here so we make it a little bit more readable or another way of talking about it is it is 1 times 10 to the seventh is the same thing as 10 million so which of these if we were to really roughly estimate we would go to 10 million well this right over here is one point two seven one million or 1 million 270 1543 if I were to really roughly estimated I might go to 1 million but I'm not going to go to 10 million so I'd rule that out this is 12 million seven hundred fifteen thousand four hundred thirty if I were to roughly estimate this well yeah I would go to ten million ten million is if I were to just if I wanted to really just look one digit to represent it if I would write this in scientific notation this right over here this right over here is one point two seven one five four three times ten to the seventh let me write that down twelve million seven hundred and fifteen thousand four hundred and thirty if I were to write this in scientific notation is one point two seven one five four three times ten to the seventh and when you write it this way say hey well if I was really estimate this and get pretty rough with it and I just rounded this down I would make this one times ten to the seventh so this really does look like our best choice now let me just verify well this right over here if I were to round it I go to a hundred million or one times 10 to the eighth that's way too big and this if I were to run it out go to a billion or one times ten to the ninth so that's also too big so once again this feels like the best answer now let's try a couple more so here we're asked how many times larger is seven times 10 to the fifth then one times 10 to the fourth well we could just divide to think about that seven times 10 to the fifth divided by 1 times 10 to the 4th well this is the same thing as 7 over 1 times 10 to the 5th over 10 to the 4th which is just going to be equal to well 7 divided by 1 is 7 and 10 to the 5th that's that's 10 being or multiplying 5 tens and then this is and then you're dividing by 4 10 so you're going to have one 10 left over or if you remember your exponent properties this would be the same thing as 10 to the 5 minus 4 power or 10 to the first power so this right over here all of this business all of this business is going to simplify to 10 to the 1st or like next write it this way this would be the same thing as 10 to the 5 minus 4 which is equal to 10 to the 1 which is just equal to 10 so this is 7 times 10 which is equal to 70 so 7 times 10 to the 5th is 70 times 70 times larger than 1 times 10 to the 4th let's do one more so here they're asking us 3 times 10 to the 9th is 30 thousand times larger than what number so once again we can divide so we have 3 times 10 to the 9th 3 times 10 to the 9th is 30 thousand times larger than what number so let's just divide by 30,000 and see what we get and here we've written something in kind of a exponential notation or which is a scientific notation actually and here we just wrote the number out so one way we could do it is we could either write this number out and then divide or we could write this in scientific notation so let's do it either way so if we were to write if we would expand the top number out if we would expand this out we could write that as 3 followed by 9 zeros 1 2 3 4 5 6 7 8 9 we put some commas here to make it readable and then we're dividing that by 3 followed by 4 zeros 1 2 3 4 and then we could cancel out the zeros we could say okay let's divide the top and the bottom by 10 let's divide it by another 10 by another 10 by another 10 and then let's see we've done all the dividing by 10 and now let's divide the top and the bottom by 3 so this would become a 1 this would become a 1 so on the bottom we're just left with the 1 and we'd have 1 followed by 1 2 3 4 5 0 so this would be 1 followed by one two three four five zeros or 100,000 now let's write it both both of these in scientific notation so 3 times 10 to the ninth I'm just going to rewrite that as 3 times 10 to the ninth and we're dividing that by 30,000 which is the exact same thing as 3 times 10 to though we have 1 2 3 4 zeros here 1 3 times 10 to the 4th or I guess I really should say we have 4 places after the 3 so 1 2 3 4 so 10 3 times 10 to the 4th and so we could divide the 3 by the 3 and then that will simplify so 3 divided by 3 is just 1 and then 10 to the 9th divided by 10 to the 4th well that's going to be 10 to the 9 minus 4 10 to the 5th this is going to be 1 times 10 to the 5th which once again is 1 followed by 5 zeros or the exact same thing as 100,000 so it's 30,000 times larger than 100,000