Conversion between metric units

we're asked how many centiliters are in 1 dekaliter so the first thing we want to do is just think about how much is a centiliter relative to a liter and how much is a dekaliter relative to a leader and I'll write the prefixes down and and really you should have these really memorize because you're gonna see these prefixes over and over again for different types of units so the prefix kilo sometimes kilo this means a thousand that means a thousand cent if you see hecto hecto means 100 deca deca means 10 if you have nothing then that just means 1 then so let's put that there then if you have deci see this means 1/10 if you have sin T sin T this means 100 if you have if you have milli this means 1,000 so let's go back to where you're having we have senti liters we have sin T right over here so a cent T liter let me write this in a different color if you have a centiliter so a sin T liter sin T liter this is equal to one hundredth of a liter one hundredth of a liter or you could say one liter for every hundred centiliters so you could also write it like this one liter for every hundred or per every hundred centiliters sin t liters send T liters so we got the sentence they're not thinking about the dekaliter so the DECA is right over here so a dekaliter deca leader means 10 it means 10 liters or another way to say it is for every 10 liters for every 10 liters you will have 1 1 dekaliter now before I actually work out the problem what's going on here we're going from we're going from a smaller unit to a larger unit so they're going many of the smaller units in one of the larger ones and we could do it multiple ways so they want to we want to essentially convert 1 dekaliter into into centiliters now we could just do it by looking at this chart or we could do it with the I guess you call it dimensional analysis making sure the dimensions work out let's do it the first way so if you have 1 dekaliter so if you have 1 dekaliter how many liters is that well that's going to be 10 let me write it over here let me scroll to them let me say so 1 dekaliter over here would be the same thing as 10 liters that's liters we're assuming that our unit is leaders here and then 10 liters is going to be how many deciliters what's going to be a hundred deciliters right because each of these is 10 deciliters and you have 10 of them so you're gonna every time you go down you're gonna be multiplying by a factor of 10 10 100 deciliters is how many centiliters well 100 deciliters you each of them are going to be worth 10 centiliters so that's going to be a thousand a thousand centiliters so we have our answer 1 dekaliter is 1,000 centiliters 1,000 centiliters now the other way the other way to do it is you could convert a deck later to liters and then convert a leader to centiliters so if we have 1 dekaliter 1 deca liter and whenever you do unit things just make sure that it makes sense you know sometimes people instead of multiplying they would divide and they'd get oh 1 dekaliter is equal to one thousandth of a cent leader and they say no no Dec leader is a much larger unit than a centiliter so one Dec leader has to be a bunch of centiliter so this should be a large number so you should always do that reality check whenever you're dealing with units but let's do it the dimensional analysis way we're starting with 1 dekaliter we want to convert it to liters so if you're converting it to liters you want the dekaliter in the denominator deca leader and you want liters in the numerator now how many liters are 1 dekaliter well or you could say well 10 Dec 10 liters is equal to 1 Dec later 10 liters is equal to 1 dekaliter so 1 dekaliter is equal to these cancel out 1 times 10 is 10 liters now if we wanted to convert this to centiliters we're gonna want the leaders in the denominator and you want the centiliters senti leaders in the numerator now how many centiliters are there per liter how many centiliters well 1 liter 1 liter is 100 centiliters centiliter is 100th of a liter notice this and this are the inverse statements they have saying the exact same thing 1 liter per 100 centiliters here writing 1 liter for 100 centiliters we've just flipped it but it's giving the same information and the reason why we flipped it is so that the leaders cancel out and then we're just left with 10 times 100 is 1,000 centiliters 1000 centiliters and we are done