What about converting units of area? Here’s

another point where people get confused. There are ten millimetres in a centimetre, but there

are not ten square millimetres in a square centimetre! Let me show you another trick to work this

out correctly every time. Draw yourself a square. Label the square with the larger units

on each side: one centimetre by one centimetre. So the area of the square then is one square

centimetre. Okay, now how many millimetres is one centimetre? It’s ten millimetres.

Label both sides. Now multiply the smaller units to get the area in square millimetres:

One square centimetre is the same as one hundred square millimetres. Let me show you that again, with the next

pair. Imagine now that this square is one metre by one metre, making an area of one

square metre. How many square centimetres is that? Well, it’s one hundred centimetres

on each side, and one hundred times one hundred is ten thousand. One square metre is ten thousand

square centimetres. So then how many square millimetres are then

in a square metre? Not a thousand, but rather one hundred times ten thousand, which makes

one million square millimetres in a square metre. Want to check that? Draw your square

again. One metre by one metre is one square metre. But each metre is a thousand millimetres

(milli- means one thousandth), so the square metre area is also one thousand times one

thousand, or one million square millimetres. Notice the way I’m saying these units, by

the way. It’s square millimetres, square centimetres, square metres, and so on. It’s

not metres squared. Square metres, not metres squared. This is actually very important.

If you say “metres squared”, you can get yourself easily confused by trying to square

the number you’ve got for the area. Thirteen metres, squared, so you go thirteen squared,

which is a hundred and sixty-nine. No, it’s not thirteen squared; it’s not thirteen

metres, squared, it’s thirteen, square metres. It’s an easy mistake to make, but it’s

also an easy mistake to avoid by simply changing your language. Square metres, square centimetres,

square millimetres. The way you say it will affect the way you think about it. Getting

the language right is really important. Okay, so now you can work out square kilometres,

right? There’s a thousand metres in a kilometre, so that’s a thousand times a thousand, which

is one million square metres in a square kilometre. That’s a very big area. It’s so big, in

fact, that we commonly use another in-between unit to measure the area of fields, farms

and properties. That unit is the hectare, abbreviated ha. You may remember that the

SI prefix h, for hecto-, means one hundred. The hectare is defined as a “hundred area”,

a square space that is one hundred metres on each side. One hundred times one hundred

gives an area of ten thousand square metres. One hectare is the same as ten thousand square

metres. Which means there must be a hundred hectares in a square kilometre, one million

divided by ten thousand. Let’s try some area conversions now. Five

square metres is how many square centimetres? Well, square centimetres are smaller than

square metres, so I need more of them: multiply. Five times ten thousand is fifty thousand

square centimetres. Does that sound like a lot? Try putting together sheets of one-centimetre

grid paper to make a total area of five square metres. How many little centimetre squares

will you have? It’s quite a lot. Fifty thousand in fact! Three hundred and twenty-two square millimetres

is how many square centimetres? Well, square centimetres are bigger than square millimetres,

so I need less of them: divide. Three hundred and twenty-two, divided by one hundred, is

three point two two square centimetres. Sixteen thousand four hundred square metres

is how many hectares? Hectares are larger than square metres, so I need less: divide.

Sixteen thousand four hundred, divided by ten thousand, is one point six four hectares. And one more. Two point seven eight square

kilometres is how many square metres? Square metres are smaller than square kilometres,

so I need more: multiply. Two point seven eight, times one million, is two million,

seven hundred and eighty thousand square metres.