### Video Transcript

Order the given masses indicated on
the cards from lightest to heaviest. 1,674 grams, one kilogram 825
grams, 1,324 grams, and one kilogram 647 grams.

We’re given four colored cards
here. And on each one, we can see a
mass. And the question asks us to order
the masses from lightest to heaviest. Now perhaps we’d normally expect if
we were looking at some measurements of mass that something that weighs a very small
amount might have a small number and something that’s a lot heavier would have a
larger number. But there’s a slight problem with
thinking like this. Can you see what it is?

The measurements that are written
on the cards are not all using the same unit of measurement. We’ve got mixed units. We’ve got two measurements in
grams. And then we’ve got two measurements
that show a whole number of kilograms and then some more grams on the end. And so if we were just looking at
the numbers on the cards, we might say that the blue card shows the smallest numbers
and 1,674 is definitely the largest number we can see. But we can’t actually say these are
the lightest and heaviest masses. The only way we can compare these
measurements together is by converting some of them so that they’re all in the same
unit of measurement.

Now there’s two ways we could do
this. One way is that we could take these
two measurements and convert them from grams into mixed units, so a whole number of
kilograms and then some more grams. That way, all the measurements on
the cards will be written in kilograms and grams. Or we could leave those two as they
are and instead take the red and the blue cards and convert them from mixed units,
kilograms and grams, into just a number of grams. And that way, all the cards will be
written as so many grams.

Now either of these two methods
would work. It doesn’t matter which one we
do. But perhaps in this question, we’ll
go with the second option. The reason is it’s going to give us
one number at the end rather than two. And it’s a bit easier to compare if
we just have one large number.

So first of all, let’s take our red
card. Let’s convert one kilogram 825
grams into just grams. And as we can see, part of our
number is already in grams. We know we already have 825
grams. So we just need to convert our
kilograms into grams, too. We know that one kilogram is equal
to 1,000 grams. And remembering this fact is really
useful because that’s all we need to convert here. We have one kilogram. And so we just need to write 1,000
grams. So the mass on the red card is
worth 1,000 grams and another 825 grams. Put the two parts back
together. And what have we got? 1,825 grams.

Let’s cross out the mass that’s
written at the moment. And we’ll write what it’s worth in
grams above. Now we just need to do exactly the
same thing with the blue card. At the moment, it reads one
kilogram 647 grams. As before, part of it is written in
grams already. That’s the 647 grams. And once again, it’s quite quick to
convert our kilograms into grams because we’ve only got one of them. That’s 1,000 grams again. And if we add together 1,000 grams
and also 647 grams, we have 1,647 grams. So we can cross through these mixed
units and write the exact same thing just in grams.

And now that all the masses are in
the same units of measurement, we can just look at the numbers. Each number has the same number of
thousands, so we’re going to need to move on and look at the hundreds digits. The smallest number of hundreds is
on the yellow card. It’s three. So our lightest weight is 1,324
grams. But we can see that the largest
digit is eight 100s, so the mass on the red card must be heaviest.

Now what about the two masses in
between? Unfortunately, we can’t split them
up by looking at the hundreds. They both contain six 100s. So we need to look at the tens
digits. And seven 10s on the green card is
greater than four 10s on the blue card. So that’s how we know 1,674 grams
is greater than one kilogram 647 grams. The masses in order from lightest
to heaviest are 1,324 grams, one kilogram 647 grams, 1,674 grams, and one kilogram
825 grams.