### Video Transcript

In this video, we’re going to look
at how to convert between area units in the metric system. For example, how we change square
centimetres or square decimetres into square metres or how we change square
kilometres into square metres.

Before we begin with our area
conversions, let’s recall some familiar metric length conversions. One centimetre is equal to 10
millimetres. One decimetre is equal to 10
centimetres. One metre is equal to 10
decimetres. And a metre is also equal to 100
centimetres. And one kilometre equals 1000
metres. We can order our units from the
largest to smallest, the largest being kilometres and the smallest being
millimetres.

If we had a unit in kilometres and
we wanted to change it into metres, we could look at our conversion and say that we
must multiply our number by 1000. From metres to decimetres, we would
multiply by 10. From decimetres to centimetres, we
would multiply by 10 and the same from going from centimetres to millimetres. If instead we wanted to go in the
opposite direction, that is, changing from a small unit to a large unit, then we do
the inverse operation. Here, we would be dividing by the
power of 10, that is, dividing by 10 or 1000.

So let’s now see how we can use
these length conversions when it comes to working out an area conversion. Let’s say we have a square of one
metre by one metre. To work out the area, we’d multiply
the length by the width. In this case, that would be one
times one. So that’s one metre squared. But what if we took the same square
and instead of measuring it in metres, we measured it as 100 centimetres. In this case, our area would be
equal to 100 times 100 square centimetres, which is 10000 square centimetres. So since our squares have the same
area, we now know that one square metre is equal to 10000 square centimetres.

To change between areas, we can use
the quick technique of squaring the length conversion. We can remember, for example, that
if we want to change metres into centimetres, we multiply by 100. If we want to go the opposite
direction from centimetres to metres, we divide by 100. So if we square the length
conversion, then if we want to change from square metres to square centimetres, we
square the length conversion. So we would multiply by 100
squared, which is the same as multiplying by 10000. To go from square centimetres to
square metres, we would divide by 100 squared, which is the same as dividing by
10000.

Let’s take a look at how we would
convert square decimetres into square metres. Let’s take a look at our two
equivalent squares. One of them is one metre by one
metre. And the other one is 10 decimetres
by 10 decimetres. The area of our square, measured in
decimetres, would be equal to 10 times 10. That’s the length times the
width. So this would be equal to 100
square decimetres. If we look at our diagram, to go
from metres to decimetres, we multiply by 10. So to go from square metres to
square decimetres, we square the length conversion, which means we multiply by 10
squared, which is the same as multiplying by 100. And to go in the opposite direction
from square decimetres to square metres, we would divide by 10 squared, which is the
same as dividing by 100.

So now, we know that one square
metre is equal to 100 square decimetres. We can add in the following metric
area conversions that one square centimetre is equal to 100 square millimetres. One square decimeter is equal to
100 square centimetres. And one square kilometre is equal
to 1000000 square metres. However, if we remember the trick
of squaring the length conversion, then we can use that alongside the metric length
conversions that we already know.

So let’s now have a look at some
examples of converting metric areas.

460000 square centimetres
equals what square metres.

Let’s start by reminding
ourselves of the length conversion that one metre is equal to 100
centimetres. If we took a square of one
metre by one metre, the area can be found by multiplying the length by the width
to give us one times one, which is one square metre. An equivalent square of 100
centimetres by 100 centimetres will give us an area of 10000 square
centimetres. We can think of this if we
wanted to change from metres to centimetres, we multiply it by 100. And we can use the rule that,
to convert an area, we square the length conversion.

Here, that means if we want to
convert between square metres and square centimetres, we would multiply by 100
squared, which is 10000. And to change from square
centimetres to square metres, we divide by 100 squared. So now, we can say that one
square metre is equal to 10000 square centimetres. So to change 460000 square
centimetres into square metres, we take our value of 460000. And we divide by 100
squared. This is the same as 460000
divided by 10000, which is 46 square metres. So the missing answer in the
question is 46.

25000000 square metres equals
what square kilometres.

Let’s start this by recalling
that one kilometre is equal to 1000 metres. This means that if we wanted to
change from kilometres into metres, we would multiply by 1000. And if we wanted to change from
metres to kilometres, we would divide by 1000. So if we wanted to convert the
area units of square kilometres to square metres, we can use the technique that
we square the length conversion. This would mean that we
multiply by 1000 squared. And if we wanted to go
backwards from square metres to square kilometres, we would divide by 1000
squared. And since 1000 squared is equal
to 1000000, that means, to convert backwards or forwards, we would multiply by
1000000 or divide by 1000000. We can also say that one square
kilometre is equal to one million square metres.

So to answer our question, we
have 25000000 square metres. And we want to change it into
square kilometres, which means we must divide by 1000 squared or divide by
1000000. And since 25000000 divided by
1000000 is 25, this means that our missing answer for our square kilometres is
25.

Use less than, equals, or
greater than to fill in the blank. Seven square metres what 700
square decimetres.

In this question, we’re
comparing areas. We know that these are areas
because the units are squared. However, we can’t compare seven
and 700 directly since the square units are different. Let’s start by writing down a
length conversion that we already know that one metre is equal to 10
decimetres. This means that, to change from
metres to decimetres, we would multiply by 10. If we want to convert an area,
we can square the length conversion. This means that if we want to
change square metres into square decimetres, we would simply multiply by 10
squared, which is the same as multiplying by 100. This means that one square
metre is equal to 100 square decimetres.

So let’s take the seven square
metres in our question and change that into square decimeters. To do this, we would take our
value of seven and multiply it by 100, giving us 700 square decimetres. So if we look at the values in
our question, seven square metres and 700 square decimetres. Well, we’ve just shown that
seven square metres is equal to 700 square decimetres. So the missing symbol in the
question must be equals.

Let’s now look at a question where
we have to order areas given in different metric units.

Arrange the areas in descending
order. 10 square decimetres, 2500
square millimetres, 150 square centimetres.

In this question, we can start
by just comparing the values of 10, 2500, and 150 because they all have
different units. We have square decimetres,
square millimetres, and square centimetres. To order and compare these
values, we would have to make all the units the same. We can choose any unit. But since we can easily change
square decimetres to square centimetres and we can change square millimetres to
square centimetres, then let’s convert them all to square centimetres. We can use the fact that one
square decimetre is equal to 100 square centimetres. And that one square centimetre
is equal to 100 square millimetres.

So let’s start by changing our
10 square decimetres into square centimetres. If one square decimetre is
equal to 100 square centimetres, this means that, to get to our value of 10,
that’s like multiplying by 10. So we can multiply the value of
100 by 10 as well. And since 100 times 10 will
give us 1000, then 10 square decimetres is equal to 1000 square centimetres. Next, let’s change two and a
half thousand square millimetres into square centimetres. Since we know that one square
centimetre is equal to 100 square millimetres, that means that if we want to
change square centimetres to square millimetres, we would multiply by 100. If we want to go the opposite
direction from square millimetres to square centimetres, we would divide by
100. So since we’re changing from
square millimetres to square centimetres, we must divide 2500 by 100, which will
give us the value 25 square centimetres.

So now, we have three areas
given in the same square units. And we need to write them in
descending order. That means from the largest to
the smallest. Out of our three areas, the
value of 1000 square centimetres is our largest one. But instead of writing that
first, we must be careful to use the original value of 10 square decimetres. The next largest value will be
150 square centimetres. And finally, our smallest value
would be 25 square centimetres, which we write in the form with its original
unit of 2500 square millimetres. And so we have the final answer
for the areas in descending order.

In our final question, we’ll look
at two areas, one given as a fraction. And we need to express the areas as
a ratio.

Area a is two-fifths square
metres. Area b is 415 square
decimetres. Express the ratio of areas a to
b in its simplest form.

Let’s start by noticing that
the areas are given in different units. The area of a is given in
square metres. And the area of b is given in
square decimetres. We will need to convert these
into the same unit. But let’s start by looking at
area a. It will be good if we could
write the fractional value of two-fifths as a decimal. We can recall that one-fifth is
equal to 0.2. So two-fifths must be
equivalent to double that, which is 0.4. So two-fifths of a square metre
is equal to 0.4 square metres. Area b is given as 415 square
decimetres. So we will need to use a
conversion between square metres and square decimetres. And that is that one square
metre is equal to 100 square decimetres.

So let’s change our area a in
square metres into square decimetres. To do this, we take our value
of 0.4. And we multiply it by 100,
giving us 40. So now, we can say that area a
is equivalent to 40 square decimetres. The question then asks us to
express these areas as a ratio, with a first and then b. So we write our values of 40 to
415. And we don’t worry about units
in a ratio. Now, we need to see if we can
write this ratio in a simpler form. We can notice that since 40
ends in zero and 415 ends in five, then both of these numbers must be divisible
by five. So dividing both sides of our
ratio by five will give us eight to 83. Since we can’t simplify this
any further, this will be our final answer.

So let’s now look at what we’ve
learned in this video. We knew the metric length
conversions between centimetres and millimetres or decimetres and metres, for
example. We have also now learned that there
are different values for converting between the area units. And we can find these conversion
values by squaring the length conversion. For example, we know that, to
change from kilometres to metres, we multiply by 1000. So to change from square kilometres
to square metres, we would multiply by 1000 squared, which is the same as
multiplying by 1000000. So here, we have our metric area
conversions. And it can be very helpful to make
a note of these so that we can use them in our calculations.