# Lesson Video: Converting and Comparing Capacity: Metric Units Mathematics

In this video, we will learn how to convert capacity units within the metric system between liters and milliliters using fractions and decimals.

15:00

### Video Transcript

In this video, we’ll learn how to convert capacity units in the metric system by converting between milliliters and liters. Let’s begin by thinking about what capacity is.

There is a little bit of a difference between what we mean when we say volume and what we mean when we say capacity. Volume is the amount of space taken up by an object, and it’s measured in cubic units, for example, cubic centimeters. Capacity, on the other hand, is the measure of an object’s ability to hold a substance, whether that’s solid, liquid, or gas. Capacity is measured in a variety of different units, for example, milliliters, liters, pints, or gallons and so on. In this video, we’ll be focusing on milliliters and liters, as these units are units in the metric system.

For example, we’ll be considering how we change a quantity in milliliters into one in liters, for example, what would 5000 milliliters be in liters. In order to find out the answer to this, we’ll need to remember one really important conversion. In one liter, there are 1000 milliliters. Let’s compare this conversion that there’s 1000 milliliters in one liter to our value of 5000 milliliters. Well, as there’s five lots of 1000 in 5000, that means there must be five liters in 5000 milliliters.

It’s also helpful to consider that if we have a quantity in milliliters that we want to change into liters, then we simply divide by 1000. To go in the opposite direction, that is, to change a quantity in liters into milliliters, we would do the inverse operation. That’s multiplying by 1000. For example, if we had been given our quantity of five liters and we wanted to change into milliliters, then we would have multiplied by 1000 to get the value of 5000 milliliters.

So now let’s have a look at some questions. And in our first question, we’ll be changing a quantity in milliliters into liters.

Write two milliliters in liters.

In order to convert between these two metric units of milliliters and liters, we’ll need to remember that there’s 1000 milliliters in one liter. This means if we’re given a quantity in milliliters and we need to change it into liters, we need to divide by 1000. It would be very tempting with a value of two to think that we need to multiply by 1000 to give us a value of 2000. However, we need to divide by 1000.

If we write our value of two into a place value grid, then it would be in the position of the ones column. We should remember that when we’re dividing by 1000, we need to move all of our digits three places to the right. This means that the two will now be in the thousandths column. But we also need to ensure that we include our placeholder zeros. Therefore, two divided by 1000 gives us a value of 0.002.

It’s often helpful to think logically if this would be a correct value for the answer. If we remember that a small spoon or teaspoon is roughly five millimeters and we consider this quantity of two milliliters on the spoon, then if we were to take a one-liter bottle and pour this quantity of two milliliters into the one liter, then there’d only be a tiny amount in the bottle. This amount of two milliliters is going to be even smaller as a proportion of the larger unit of liters. We can, therefore, give the answer that two milliliters is equal to 0.002 liters.

We’ll now have a look at another question. And this time, we’ll convert a capacity in liters into one in milliliters.

Express 1.025 liters in milliliters.

In order to change this quantity in liters into one in milliliters, we need to remember that in one liter, there are 1000 milliliters. We can also think of this in terms of if we have a quantity in liters that we want to change into milliliters, we need to multiply it by 1000. We, therefore, need to multiply 1.025 by 1000. And sometimes it can be helpful to use a place value grid to help us.

We know that 1.025 is made up of one ones, zero tenths, two hundredths, and five thousandths. When we multiply by 1000, we move every digit three places to the left. Starting with our digit of one in the ones column, then this will move into the thousands column. The other digits follow behind it. And therefore, we’ve found that 1.025 multiplied by 1000 is 1025. Therefore, 1.025 liters is equal to 1025 milliliters.

As a quick check, our value of 1.025 liters is approximately one liter. Therefore, our answer will be approximately 1000 milliliters, so it must be 1025 milliliters.

In the next question, we’ll see how we can order a number of different capacities when they’re given with different units.

Arrange in descending order: 3.9 liters, 6600 milliliters, 6.9 liters, 2800 milliliters.

The first thing we should notice here is that we’re given quantities that have two different units. Some are given in liters and some are given in milliliters. Before we can put these in order, they’ll need to be in the same unit, so we can either change them all to liters or all to milliliters. Either way, we’ll need to remember the important conversion that in 1000 millimeters, there’s one liter.

So let’s take our liter quantities and change these into values in milliliters. To change a quantity in liters into milliliters, we can multiply by 1000. So let’s take our value of 3.9 liters and multiply 3.9 by 1000. When we multiply by 1000, we move all our digits three places to the left. So our value will be 3900 milliliters. 6600 milliliters is already in milliliters, but we’ll bring it down so that we can compare it in a second.

6.9 is a value in liters, so once again we’ll need to multiply it by 1000 to find the equivalent value in milliliters. Once again, we move all of the digits three places to the left when we’re multiplying by 1000, so this will give us 6900 milliliters. Finally, we have the value of 2800 milliliters.

Now, let’s put these four values in order, but we must be careful. We’re told that it should be in descending order. That’s from the largest value to the smallest value. Looking at our four quantities then, we could see that the largest one is 6900 milliliters. But we should be careful as we want to give it in its original form. That’s 6.9 liters. Going down in size then, our next quantity would be 6600 milliliters, which we can write in the same way as it was originally given. Next, we have 3900 milliliters, which we’ll write as 3.9 liters. And so we’re left with one value, 2800 milliliters. And we can check that it is indeed the smallest of these values.

We can, therefore, give the answer that these quantities in descending order are 6.9 liters, 6600 milliliters, 3.9 liters, and 2800 milliliters. In this approach, we changed all of our values into a quantity in milliliters. We could have also changed them all into liters. 3.9 liters and 6.9 liters would have stayed the same. 6600 milliliters would have been 6.6 liters. And 2800 milliliters would be 2.8 liters. The largest value in liters would still be 6.9 liters, followed by 6.6 liters — which is 6600 milliliters — followed by 3.9 liters, and finally, our quantity of 2.8 liters, which was 2800 milliliters. And so we’ve confirmed our answer.

In the next question, we’ll see how we might need to convert the units before carrying out a calculation.

Write the answer in milliliters: 3.15 liters plus 6250 milliliters.

When we see a question like this, it can be tempting to rush in and start the addition straight away. However, we should notice that we have two quantities that are given in different units. One is in liters and the other one is in milliliters. In order to add these, they’ll need to be in the same units. We could either change them both into liters or both into milliliters. But we’re asked to give the answer in milliliters, so it would be sensible to change them both into milliliters.

We should recall that in one liter, there are 1000 milliliters. As we’re changing a quantity in liters into one in milliliters, we’ll therefore need to multiply by 1000. So 3.15 multiplied by 1000 will be 3150. When we’re multiplying by 1000, we move all of the digits three places to the left.

Now that our two quantities are in the same units, we can add them. 3150 plus 6250 gives us 9400. Therefore, we can give the answer in milliliters of 9400 milliliters.

Let’s have a look at another question in a real-life context.

If five liters of water is going to be poured into 200-milliliter bottles, how many bottles will be used?

Let’s start by thinking about this problem. Let’s imagine that we have our five liters of water in five of these liter containers. If we then poured all of these five liters of water into a number of different 200-milliliter bottles, how many bottles will we need? It’s difficult to answer in this format as we have quantities given in different units, ones in liters and the others in milliliters. So we’ll need to use the conversion that one liter is equal to 1000 milliliters.

This means that five liters is equal to 5000 milliliters. And we can verify this in two different ways. We can multiply our quantity in liters by 1000 to get 5000. Or, as an alternative, we can recognize that each of the one liters would be equal to 1000 milliliters, so five of those would be 5000 milliliters.

Now we need to work out how many 200 milliliters there are in 5000 milliliters. We can do this by dividing 5000 by 200. This is equivalent to 50 divided by two. And that’s equal to 25. So our answer is that we need 25 200-milliliter bottles.

We can check this by thinking about how many bottles would be required for one liter of water. As each 1000 milliliter, or one-liter quantity, has five lots of 200 milliliters, then each one liter will need five bottles. Five lots of five bottles would give us 25 bottles.

Let’s have a look at one final problem question.

Each week a family consumes six 693-milliliter bottles of orange juice. Determine, in liters, the amount of orange juice in each bottle.

It can be very easy to read a question like this and try straight away to multiply six by 693. However, if we read the question a little more carefully, we’re asked for the amount of orange juice in each bottle and not in six bottles. Each bottle has a capacity of 693 milliliters, but we need to give this value in liters.

We can recall that 1000 milliliters is equal to one liter. If we have a quantity in milliliters and we want to change it into liters, we must divide by 1000. In order to do a calculation such as 693 divided by 1000, it can be helpful to use a place value grid. 693 can be written as six hundreds, nine tens, and three ones. And to divide by 1000, we move each of our digits three places to the right.

The digit three then moves from the ones column to the thousandths column. The digit of nine also moves three places to the right into the hundredths column. And finally, our digit of six moves into the tenths column. We must remember to include our zero as a placeholder before the decimal point. So 693 divided by 1000 is 0.693. Therefore, we can give our answer that each 693-milliliter bottle is equivalent to 0.693 liters.

We can now summarize what we have learnt in this video. Firstly, we saw how capacity is the measure of an object’s ability to hold a substance. Metric units of capacity include milliliters and liters. To convert between liters and milliliters, we use the conversion that one liter is equal to 1000 milliliters. This is a conversion that is usually required to be learnt for examinations.

This conversion means that if we have a quantity in milliliters and we want to change it into liters, we divide by 1000. If we want to change a quantity in liters into one in milliliters, we must multiply by 1000. When we’re doing any sort of conversion with metric units, we’ll often need to multiply or divide by powers of 10, for example, 1000 here. Using a place value grid can be helpful in our calculations.