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CCSS.Math:

so I have two conversion scenarios right over here I want to convert three kilograms into milligrams and I want to convert four tons into ounces so this is clearly in the metric system and this right over here is in the US customary system so I encourage you to pause this video and try to do these conversions on your own well to think about this one we just have to think about what these what these prefixes mean so I could rewrite it this this is three kilograms kilograms and we're going to convert into some amount of milligrams milligrams and we've already seen that the prefix kilo this literally means 1000 this means 1000 and the prefix milli the prefix milli means 1 over a thousand or one thousandth of a gram so let's just convert to grams first let's go from kilograms to grams and then we can go from grams to milligrams so we could say that three kilograms three kilograms is going to be equal to three times 1,000 three times 1,000 grams three times 1,000 grams so that's three thousand grams so this is equal to three thousand three thousand grams this is literally three thousand grams that's one way to interpret kilo so this gets us to three thousand grams now how do we go from the grams to the milligrams well we already said we already said right over here that one milligram let me write it if your 1 milligram is equal to one over a thousand or one thousandth of a gram but another way of thinking about this statement is that one gram is equal to one thousand milligrams so if we keep this in mind we have three thousand grams each of those are going to be equal to one thousand milligrams so this is equal to three thousand three thousand grams each of those are equivalent to one thousand milligrams so times 1000 times 1000 and this is going to give us the number of milligrams and what is this going to be well three thousand one thousand a thousand thousands is a million so three thousand thousands is three million so this is going to get us three million three million milligrams another way to think about this multiplication I've got I've got three zeros here three zeros here so my final product should so 3 times 1 is 3 and then I should follow that with the 6 0 so I get 3 million milligrams now let's do the same thing over here let's convert this this US customary ton right over here to ounces and what we'll do first is we'll go 2 pounds and then from pounds we can go 2 ounces and we know we know that 1 ton is equal to 2,000 2,000 pounds so 4 tons 4 tonnes are going to be equal to well each of those are going to be 2,000 pounds it's going to be 4 times 2,000 pounds which is equal to 8,000 pounds 8,000 make sure have some space here 8,000 pounds 8,000 pounds now how many how many Ounces are in each of those pounds well we know that 1 pound we know that 1 pound is equal to 16 ounces so 8,000 pounds so this over here so let me write this so 8,000 pounds 8,000 pounds if each of those 8,000 has 16 ounces are equivalent to 16 ounces this is going to be 8,000 times 16 ounces so what is 8,000 times 16 so this is going to be let's see 8 times 16 is 80 plus 48 is 128 but then that's not 8 we want to do 8,000 times so it's going to be 128 thousand one hundred and twenty-eight thousand ounces so four tonnes are a lot of ounces