 So let's consider some non-standard bases. Up to now we've been looking at operations in base n, where every unit is n times larger than the preceding unit. But there's quite a few common situations where this is not the case. For example, time. In timekeeping we have 60 of the smallest units making up one of the next larger unit, that's one minute. Then we have 60 of these minutes making up one hour. And then we take 60 hours and we don't actually have a unit name for 60 hours. In fact, the next larger unit of time is going to be formed by taking 24 of these hours to make one day. And then we might take 7 of these days to make one week. And note here that our trade rate changes from 60 to 1, 60 to 1, to 24 to 1, to 7 to 1. A similar situation occurs when we look at dairy products. So I have 12 units making up a dozen, 12 dozen making up a gross, 12 gross making up one great gross, but I don't have a name for anything more than 12 great gross. The metric system even has some irregularity to it. So in the metric measurements I have commonly used units like centimeters and meters, 100 centimeters form one meter, but the next commonly used unit is not 100 meters. Trivia question, what do you call a unit of 100 meters? But in fact what we do is we take 1,000 meters to form the next higher commonly named unit, the kilometer. And after kilometers we don't have any generally used common names. And then there's even more peculiar systems that are used in certain obscure countries that nobody can ever seem to find on a map. These are places like Myanmar and Liberia and the United States. Yes, the United States, where we have this strange system where we take 12 inches to make one foot, and then we change to a totally different trade rate, 3 feet to make one yard. And then there's a whole bunch of other units that nobody ever remembers the conversion rates for. 5,280 feet make up one mile. However, it's not a problem. We can work with these non-standard bases just as easily as we can with other bases. For example, let's take a unit like 357 centimeters and try to express this in simplest way. What that means is that whatever we have left, we cannot make a trade to any larger unit. So we need to know the bundle and trade rate. 100 centimeters can be traded for one meter. And we can start out by setting down a place value chart and for reference we'll keep our trade rates there. So we have centimeters, 100 centimeters make up a meter. Who knows? We might need it. 1,000 meters make up one kilometer. Now what we have, 357 centimeters. We'll put that in our centimeter column. Note that we are not going to indicate the unit of centimeters. It's 357. The unit is indicated by the fact that it's in this column labeled centimeters. So now we can try to bundle and trade. So our trade rate, 100 centimeters. So we look for bundles of 100 centimeters and we split them off. So here I might take that 357 and split off a couple of hundreds to three. So there's our 1, 2, 300 centimeters. 57 is what's left over. And now I can trade. 100 centimeters will get me one meter. So I'm going to trade 100 centimeters for one meter, 100 centimeters for one meter, 100 centimeters for one meter. And I can combine these. 1, 2, 3 meters. And I don't have enough centimeters to trade for a meter. I don't have enough meters to trade for a kilometer. So we're done with our conversion. And so now this final answer, three meters, 57 centimeters. We can also do this much more horrendous problem, 389,195 centimeters. And we can do the same thing. We'll set down our trade rate. We'll set down our place value chart with the trade rates included. We'll drop down our 389,195 centimeters and we'll make the trades 100 centimeters at a time for one meter. Well, I'll split off a whole lot of centimeters. So this is 3,891 centimeters. And at my trade rate 100 centimeters for one meter, I'll go ahead and trade those over as 3,891 meters. Again, I can trade again. 1,000 meters make up one kilometer. So I'll split off a few thousand meters. So there's a 3,000 meters split, 891 left over. And I'll trade 1,000 meters for one kilometer. This 3,000 meters becomes one kilometer. And so again, not enough centimeters to make a meter. Not enough meters to make a kilometer. And so I'm done. And so the equivalent form, 3 kilometers, 891 meters, 95 centimeters. We could even do this with the peculiar system that we use in this country. 40 inches in simplest form. Let's take a look at that. So here our units are going to be yards, three feet, make up a yard, foot, 12 inches make up one foot, and then inches are the smallest units that we have. So we're dealing with 40 inches. We'll drop that in the inches column and we'll split off this time sets of 12. So we'll bundle a set of 12 and another and another. And we'll trade 12 inches gives us one foot, 12 inches gives us one foot, 12 inches gives us one foot. And there we have our feet. We'll combine them. And so we do now have enough feet to make up one yard. So three feet we can trade for one yard. And our final answer is going to be one yard, zero feet, four inches.