Converting metric units
We're asked to arrange the following measurements in order from smallest to largest. And we have the measurements, and they're different units. This is in decameters, then we have meters, then we have millimeters, then we have centimeters. So the way I would tackle this is I would try to convert them all to the same units, maybe meters, and then compare them all in terms of meters. So let's do that. So this is just a screenshot of that exact same screen we just saw there. And so let's just convert each of these into meters. So the first one we have right over here is one decameter. So we have to remind ourselves what deca even means. Well, deca is equal to 10 meters. And actually, let me add more of these, just so that we know all the different prefixes we could have. So you have deca. You have hecto, which would be 100. You have kilo, which would be 1,000. And then, of course, you just have meters, and you'd have no prefix there. That would just be equal 1 if you have no prefix in front of the meters. And then if you have a tenth of a meter, that is decimeter, so this is 1/10. Then you have centi, which is 1/100. And then you have milli, which is equal to 1/1,000. So let's use this information right over here to figure out how many meters each of these are. So one decameter-- we just saw deca means 10. That's 1 times 10 meters. So this is going to be equal to 10 meters. So this right over here is 10 meters. This is already written in meters. This is 13 meters. Then we have 15,000 millimeters, but milli means 1/1,000, So it's 15,000 times 1/1,000 of a meter. So each millimeter is 1/1,000 of a meter. You could view this as instead of writing a milli here, I wrote 1/1,000. So 15,000 times 1/1,000, that's just going to give me 15. So this is going to be 15 meters. So this is 15 meters. Another way of thinking about it is, look, 1,000 millimeters is equal to a meter. So let's divide this into groups of 1,000. Well, this is literally 15 groups of 1,000. This is 15 groups of 1,000 millimeters, so that's going to be 15 meters. And then, finally, we have 1,900 centimeters. So 1,900, instead of writing centi, I'm going to write 1/100 of a meter. Well, 1,900 times 1 over 100 is 19, so this is equal to 19 meters. Another way of thinking about it is, this is 19 groups of 100 centimeters, and 100 centimeters is equal to a meter. This is 19 meters right over here. So let's go back to the actual problem. So let's remind ourselves. This right over here, this is 10 meters. This is 13 meters, so 10, 13. This right over here was 15 meters, and this right over here was 19 meters. So actually, the order that they already gave it to us in, we could obviously swap things around if we wanted to. But the order that they already gave it to was the order from smallest to largest. This is 10 meters, 13 meters, 15 meters, and 19 meters.