Lesson Video: Converting and Comparing Mass: Metric Units Mathematics

Video Transcript

In this video, we’re going to convert, compare, and order mass units in the metric system, for example, kilograms, grams, milligrams, and tons. We’re going to look at how we can apply this in real-world problems. We can begin by thinking about what we mean by mass. Mass is how much matter is in an object. So how does this compare to the weight of an object? Well, weight is a measure of the force of gravity acting on an object. In everyday life, we often talk about the weight of a person or the weight of an object. But in reality, what we’re really talking about is the mass of a person or the mass of that object.

A helpful way to illustrate the difference between mass and weight is if we have a person of mass 70 kilograms, then they’re going to have the same mass whether they’re on Earth or on the Moon. Both masses would be 70 kilograms. The weight of this person, however, would change. They would weigh more on Earth than on the Moon because the force of gravity is much stronger on Earth. So in terms of the units that we use to measure mass, we can see how kilograms would be one of them. But what other units are there? Along with kilograms, we also have grams, milligrams, and metric tons. You will also be familiar with some other units of mass: ounces, pounds, and stones.

In this video, we’re just looking at the metric units of mass. That’s kilograms, grams, metric tons, and milligrams. So let’s look at ordering these in order of the smallest unit to the largest unit. If we have an object that is small and light, we may choose to measure this in milligrams. If we have an object that’s much larger, for example, a car, we might choose to measure this in metric tons. As an aside, in some parts of the world, tonnes with an extra “ne” is used instead of metric tons. But in both cases, the symbol “t” can be used to signify this.

In order to think about converting between units in the metric system, let’s begin by looking at how we change milligrams into grams. In one gram, there are 1000 milligrams. So that means if we have a unit in milligrams and we want to change it into grams, we would divide by 1000. If, instead, we had started with a unit in grams and we wanted to change it into a unit in milligrams, then we’d multiply by 1000. To convert between grams and kilograms, we can recall that in one kilogram, there are 1000 grams. So if we start with our unit in grams and we want to get to a unit in kilograms, then we would divide by 1000. In the opposite direction, if we have a unit in kilograms and we want to change it into grams, then we would multiply by 1000.

Finally, between tons and kilograms, we have 1000 kilograms in one ton. In the same way, if we had a unit in kilograms and we wanted to find its equivalent in metric tons, we would divide by 1000. Or if we’d started with a unit in metric tons and we wanted to find its equivalent in kilograms, we would multiply by 1000. The conversions that we’ve written here are generally something that needs to be learnt. Sometimes, the difficulties in a topic like this can come from place value and actually understanding how to multiply and divide by 1000, particularly when there are decimal numbers involved. In the following questions, we’ll look at converting between metric units of mass. But we’ll also take a closer look so that we have a better understanding of the place value when multiplying or dividing. Let’s begin with our first question.

How many grams are in 12 kilograms?

In order to be able to answer this question, we need to remember a key conversion. And that is that in one kilogram, there are 1000 grams. So, if one kilogram is 1000 grams, two kilograms would be 2000 grams, three kilograms would be 3000 grams, and so on. We can think of if we have a unit in kilograms and we want to change it into a unit in grams, we would multiply it by 1000. So therefore, the value of 12 kilograms would be 12 times 1000, giving us our answer of 12000 grams.

Let’s have a look at another question involving a decimal number conversion between milligrams and grams.

Fill in the blank. 746.8 milligrams equals what grams.

In this question, we need to convert between two metric units, milligrams and grams. We can recall that in one gram, there are 1000 milligrams. So that means if we have a unit in milligrams and we want to convert it into grams, we must divide by 1000. If we take our value of 746.8 milligrams and consider how we would divide by 1000, it can be helpful to think how our digits would move in terms of the place-value columns.

When we divide by 1000, that’s the same as our digits moving three columns to the right. So the seven would move once, twice, three times. The digits of four, six, and eight will also move three places to the right. But we must remember to fill in our decimal point and a placeholder of zero. So we have the answer of 0.7468 or seven thousand four hundred and sixty-eight ten thousandths. And that’s the missing answer in grams. That’s equivalent to 746.8 milligrams.

In the next question, we’ll look at how we can compare masses given in different units.

Use less than, equals, or greater than to fill in the blank. 0.2 kilograms what 276 grams.

In this question, instead of simply comparing the values, there’s the added complexity that the units given are different. We have kilograms and grams. In order to compare these two values, we need to make sure that they’re in the same units. We can use the conversion that one kilogram is equal to 1000 grams. So if we have a unit in kilograms that we want to change into a unit in grams, we would multiply by 1000. If we want to go in the reverse direction with a unit in grams and convert it into a unit in kilograms, then we’d divide by 1000.

So if we look at our two values, we can either change our units in kilograms into grams or change our unit in grams into kilograms, but we don’t need to change them both. In this case, we could look at changing 0.2 kilograms into unit in grams. So we take the 0.2 and multiply by 1000. If we consider 0.2 written in a grid like this with our two in the tenths column, when we multiply by 1000, what we need to do is move this two three places to the left. So now the two is in the hundreds column. But we can’t leave it there on its own without some placeholders because that two represents two hundreds. So now we know that 0.2 kilograms is the same as 200 grams.

We can then easily compare 0.2 kilograms, or 200 grams, with 276 grams. Which one is bigger? Well, it’s the 276 grams. So we’re going to use the less than symbol because 0.2 kilograms is less than 276 grams. And that would be our answer, the less than symbol. So what would have happened if we changed 276 grams into kilograms instead? In this case, we would have been dividing by 1000 to give us 0.276 kilograms. We can still see that 0.2 kilograms is less than 0.276 kilograms, confirming our answer of less than.

In the next question, we’ll look at carrying out a calculation where the masses are given in different metric units.

Write the answer to the calculation in grams. Three and three-quarter kilograms subtract 640 grams.

When we look at this question, we notice that our masses are given in different units. We have a value in kilograms and a value in grams. We therefore need to convert between the two units. We’re asked to give the answer to our calculation in grams, so it will be sensible to change this unit in kilograms also into grams. We can recall that in one kilogram, there are 1000 grams. When we have a value like three and three-quarters with a fraction, there are several different ways in which we can think of converting this into grams. One way might be by splitting our three kilograms and our three-quarter kilograms. If one kilogram is equal to 1000 grams, then we would take our unit in kilograms and multiply it by 1000 to get the equivalent in grams. So therefore, three kilograms would be three times 1000 grams. And that’s of course 3000 grams.

To work out three-quarters of a kilogram into grams, that would be working out three-quarters of 1000 or three-quarters times 1000. We might recall that a half of 1000 is 500. So a quarter of 1000 would be the same as half of 500. And that’s 250. So in order to work out three-quarters of 1000, we could think of it as multiplying a quarter by three or, indeed, by adding a half and quarter. Either of those would give us 750 grams. So if three kilograms is 3000 grams and three-quarters of a kilogram is 750 grams, adding those together would give us that three and three-quarter kilograms is 3750 grams.

The other approach to this question is to work out what three-quarters is as a decimal first. As three-quarters is equal to 0.75, then three and three-quarters is 3.75 kilograms. In order to change this value into grams, we’re still going to need to do the same multiplication by 1000. When we multiply by 1000, we move our digits three places to the left, which will give us 3750 grams, the same as we calculated in the first method. We can then go ahead and work out the answer to this subtraction. 3750 subtract 640 gives us the answer in grams of 3110 grams.

In the next question, we’ll look at ordering masses given in three different units.

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.

In the final question, we’ll look at a story problem involving masses.

Noah bought two and one-quarter kilograms of carrots and four and one-quarter kilograms of apples. How many grams of food did he buy?

Let’s begin this question by writing the value of the kilograms of carrots and apples in a more mathematical way. We’re told that the mass of carrots is two and one-quarter, which we can write as the whole number two and a fraction of one-quarter. The units of mass is the metric unit of kilograms. Noah also bought four and one-quarter kilograms of apples, so we can write that as four and one-quarter. We have the same units of kilograms. We’re asked to work out how many grams of food; that’s the total mass. We notice here that we’re asked in terms of grams rather than kilograms. We can approach this in two ways. We could either convert both of these masses in kilograms into grams and then add. Or we could add them first and then convert to grams.

Here, I’m going to add them first. In order to add two and a quarter and four and a quarter, we can add the whole numbers of two and four, giving us six. We can then add a quarter and a quarter, giving us two-quarters. But we can also simplify this fraction to one-half, so we know that the total mass is six and a half kilograms. We can recall that in one kilogram, there’s 1000 grams. When it comes to converting six and a half kilograms, it’s helpful to remember that the decimal form of this would be 6.5 kilograms. So we have 6.5, and we multiply it by 1000 to find the mass in grams, which is 6500 grams. And so we’ve answered the question that Noah bought 6500 grams of food.

We’ll now summarize what we’ve learnt in this video. At the beginning, we saw how mass is how much matter is in an object. We looked at four different metric units of mass, milligrams, grams, kilograms, and metric tons. We saw the three key conversions between metric units of mass. These will often be required to be learnt for exams. And finally, as we saw in a number of questions, in order to compare or order masses, we must make sure that the masses are in the same unit. We can make sure that these masses are in the same unit by converting them using these conversions given.