 Converting between measures such as millimetres, centimetres, metres and kilometres is common place in our lives. The process is made nice and simple because of the metric system, which was first proposed by the French astronomer and mathematician Gabriel Mouton in 1670 and relies on powers of 10 to link varying magnitude of length, area, volume and more. We consider the metre to be our base unit, linking in other magnitudes by shifting powers of 10. For example, one kilometre is three powers of 10 larger than one metre. Therefore, to change from metres to kilometres, we need to divide the metre value by 10 three times. Looking at the smaller end of the scale, we have millimetres. The prefix mille denotes a factor of one thousandth. Therefore, a millimetre is one thousand times smaller than a metre. To convert metres to millimetres, we therefore multiply by one thousand. As the prefix mille means one thousandth, the prefix centi means one hundredth, so a centimetre is one hundredth of a metre. All of this information is very much well known, yet when we start to look at area and volume, there are often some misconceptions. We know there are 100 centimetres in a metre, but how many centimetres square are there in one metre square? Pause if you think you can work it out. It's often thought that because there are 100 centimetres in a metre, that the same applies to centimetre square in a square metre. However, we have to consider what square metre means. Simply put, a square that has lengths of one metre. We know that because one metre is the same as 100 centimetres. That our square dimensions are 100 centimetres by 100 centimetres. We find the area of a square by multiplying the base by the height, which means that one metre squared contains ten thousand centimetres squared. We can therefore convert any values in metre squared to centimetre squared by multiplying the value by four powers of ten, or back by dividing by four powers of ten. See if you can convert this value in centimetre squared to metre squared. To convert four thousand five hundred centimetres squared to metre squared, we need to divide four thousand five hundred by ten four times. This gives us an answer of zero point four five metres squared. As you can see in this conversion chart, we can convert between each of the forms using powers of ten. This time however, the powers of ten for each conversion are double that they were for lengths. This is because area is found by taking lengths in two dimensions. With this in mind, how many centimetres cubed are there in one metre cubed? Pause the video to see if you can work it out. As with one metre squared, we need to consider what one metre cubed means. A one metre cubed cube is made up of three dimensions, each one metre in length. As we know, one metre equals one hundred centimetres, so we can calculate our volume by multiplying these together. There are therefore one million cubic centimetres in one cubic metre. With area, we found our powers of ten by doubling the length powers. Because volume adds a third dimension, we can find our volume powers of ten by multiplying the length powers by three. This can be seen here in the conversion table for lengths, areas and volumes. The final conversions we are going to look at are converting cubic measurements into capacities, looking at how many centimetres cubed there are in a litre. A litre is defined as the volume of one kilogram of water, and we also know that one centimetre cubed of water is the same as one milliliter of liquid. As we learnt, milli refers to a thousandth, so there are one thousand millilitres in a litre. This also therefore means that one litre of liquid is one thousand centimetre cubed. With this information, see if you can figure out how many litres there are in one metre cubed. Because we changed from cubic centimetres to cubic metres by dividing by ten six times, we can see that if one litre contains one thousand centimetres cubed, it's then equal to zero point zero zero one metres cubed. We can also see that because zero point zero zero one metres cubed is one thousandth of a litre, there must be one thousand litres in one metre cubed. Understanding all of these conversions can be tricky at first, but if you can link the number of dimensions to the change in powers, you'll be giving yourself a head start.