Video: Arranging Masses in Ascending Order by Converting Their Units

Arrange in descending order: 2,700 kilograms, 5,450 kilograms, 840,000 grams, 3(1/4) metric tons.

03:35

Video Transcript

Arrange in descending order. 2700 kilograms; 5450 kilograms; 840000 grams; three and a quarter metric tons.

When we’re answering a question like this, it might be very easy to look at the numerical values and simply try and order these. The important thing to notice here, however, is that the units of the mass are different. We have, in fact, got three types: kilograms, grams, and metric tons. Note that the metric tons here is also known as tonnes spelt with an extra n and e in different parts of the world. We can only order these masses whenever all the units are the same. If we were to order our three units in terms of descending size, we’d have tons as the largest, then kilograms, and then grams as the smallest. By that we mean that one ton is bigger than one kilogram, and one kilogram is bigger than one gram.

When it comes to writing these in the same units, we could choose any of the units of tons, kilograms, or grams to write each value in. However, here we already have two given in kilograms, so it might seem sensible to change all of these masses into a value in kilograms. So how do we change a value in tons into a value in kilograms? We can recall that one metric ton is equal to 1000 kilograms. We could then say that to change a value in tons into kilograms, we would multiply by 1000. So if we have three and one-quarter tons, we could begin by writing this as 3.25 tons. And that’s because a quarter as a decimal is 0.25.

To work out this value in kilograms, we have 3.25 multiplied by 1000. When we’re multiplying by 1000, we move all of our decimal digits three places to the left, giving us 3250 kilograms. As a check that our value is roughly correct, if we imagine that we just had three tons, when we multiply three by 1000, we’ll have 3000. So 3250 kilograms here would be in the correct order of magnitude. Next on our list of masses, we need to change 840000 grams into a value in kilograms. The conversion we need here is that in one kilogram, there’s 1000 grams. So when we start with a value in grams, we must actually divide by 1000 in order to get the equivalent in kilograms. So 840000 grams is equal to 84,000 divided by 1000 kilograms, which we can write as 840 kilograms.

And now we have all four masses as a value in kilograms. To arrange in descending order means that we start with the largest mass first. So that will be 5450 kilograms. The next largest will be 3250 kilograms. But we must write that in the original way it was given, as three and a quarter metric tons. Next, it’s 2700 kilograms. And finally, the smallest value of 840 kilograms, which we write in the original format of 840000 grams. And that’s our list of masses given in descending order.