Friday, 10 April 2009

Check your units

Units are useful things. If you want to use maths practically then you will need some units. Measure a window and you need to know if you are talking about 10centimetres 10metres 10 inches or 10 feet. Let's take that window and say that it is a square 10cm by 10cm. The area of the window is 10 x 10 centimetres squared. Let’s be clear that you understand this. Can you picture a square that is 1cm by 1cm? If you had a line of 10 of them you would have 10 squared centimetres. However if you have a length of 10 of these squares and then make it a big square with a 100 of the small squares in total, then you have 100 squared cms = 10cm squared. If you are not sure about this then read it again.

Areas can metres squared or inches squared or any length squared. If you have any area then your units have to be a length squared. So a formula (see last blog) like 2πr only has one unit found in the radius. Π is a number 2 is a number and neither have units. There is one unit of measurement so you must be talking about a length. It is indeed the formula to find the circumference of a circle. If you had a formula π times the radius squared then you have units of length times the units of length. It tells you that it is an area, and this formula is in fact the area of a circle.

If you write down some workings in mathematics then you should always check them if you have time. If you don’t have time then at least check the units so that your length is not measured in seconds.

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