## Square Units

The shape below is a square and has sides of 1 cm. The area for the square is; Suppose we wanted to use mm instead of 1cm. The units have been converted from cm to mm below; The area in mm is now; It is therefore logical to say that 1cm² is equal to 100mm ². With knowledge of the fact explored above you can use the fact to convert areas for example; …and… Let’s look at a different unit. Below is a square with sides of 11km. The area for square is; Suppose we use metres instead of kilometers. Below the square the square units have been converted to metres. The above shows us that; Suppose the above value is so big it is a good idea to use standard form. In this example we can use the conversation to work out that; Here is another example; Above you may have noticed a pattern which we can use as the general when dealing with square units. In general when dealing with square units you need to square the conversation factor too for example; …that means; Here is another example; …that means…## Cubic Units

The cube below has edges of 1cm. Suppose we wanted to find the volume. The volume would be; What if we converted the units from cm to mm. The cube units have been changed to mm as shown below; The volume in mm would now be; We can conclude that; Let’s explore an example for the above conclusion. Here is another example;### Capacity problem

Here is an example based on what is explored above. An oil tank is in the shape of a cuboid. It measures 5m x 4.7m x 3.3m. How many litres of oil can the tank hold when full? We know that; First we calculate the volume of the tank in m^{3}so the volume is; Next we convert the units into cm

^{3}Every 1000cm

^{3}makes 1 litre therefore; So the volume is 7.55 x 10

^{3}litres we can convert the number into standard from at the moment it is not. When writing standard forms the number at the front needs to be between 1 and 10. So we must divide 77.55 by 10. Since we divided 77.55 by 10 we must increase the power at the end by 1 to compensate. Or simply multiply 10

^{3}by 10 since we divided. The result is;