Unit symbols & use

When units are altered by mathematical operations we end up with a derived unit, which is simply a combined unit. You are already used to using some of these already, like miles per hour, which is a derived unit because it is a combination of 2 other units. 

• For example, we all know that when finding the speed of a car that travels 300 miles in 5 hours we divide 300 miles by 5 hours and we get the answer of 60 miles per hour. When we write this algebraically it will look like this: 

• Tip: Derived units will be easier to process when performing math functions if you write them in fractional form as the example answer has the mi on top and the h of the bottom of a fraction instead of writing an abbreviation like mph or using a slash notation like mi/h. 

Disco converting: Converting units 

Multiplying by a conversion factor allows us to change units without changing the value of a quantity. 

If you need to convert from 10 cm to meters do you multiply or divide? Instead of asking that question, prove it by looking up a conversion factor and build a fraction. Since the 100 cm and  1 m are equal, the value of both of these fractions (100 cm / 1 m) and (1 m / 100 cm) are equal to 1. That means that we can multiply any quantity by these fractions without changing the value (since anything times 1 is the same value as the original quantity). 

We can check to see how/if the conversion works by DISCO CONVERTING, to see if units cancel out to leave the desired unit at the end of the conversion. The idea comes from the disco dance move where you point up to one side and down to the other. If you want a unit to cancel out you need it to show up in the top of the one part of the equation and in the bottom of another part (assuming they are on the same side of the equal sign). 

 To disco convert you write the original value first, then select the fraction for the conversion that will cancel out the units you are getting rid of an leave the ones you want. In the top example the 10 cm is multiplying the 100 cm and divided by 1 m, resulting in 1000 cm^2/m, which is not a simple distance unit. In the second case, the conversion is set up so the cm from the 10 cm cancel with the cm in the bottom of the fraction, leaving a simple meter of the units.