Tuesday, 20 September 2011

Two Step Conversions!

Last class, we learned about the basic unit conversions. You might think it's simple, however, it is the fundamental basics which you would need in order to do future conversion problems. Today, we learned about not one step, but two step conversions!

What is it, you may ask?

Well, for more complicated conversions, you would have to convert more than once to get to your designated unit. Convert it to the 10^0 prefix which are grams, meters, seconds, and Litres. To do this, you would have to have a "travel route":

Eg. Converting 50km into cm:
km -> m -> cm

You would have to convert kilometers to meters first, then convert that to centimeters.

50km x 1000m/1km x 100cm/m = 5000000cm


NOTE: Always have the unit you want to cancel on opposite sides of the fraction!! Also, leave the answer in scientific notation if the answer is either too large or too small. (eg. 5000000cm = 5.0 x 10^6cm)

Eg. Convert mg to dg:
We would have to first convert mg to grams, then from grams to decigrams.


Derived Quantity Conversions

  • it is when there is more than one SI base unit in a single quantity 
         Eg. 10km/h or 10m²  
  • convert to the unit on the numerator first then convert the denominator

    Eg. 10km/h to cm/s:

    10km/h x 1000m/km x 100cm/m x 1h/3600s
    Then you can cancel all the units you have repeated until you are left with cm/s


  • if the unit is squared or cubed, you will have to multiply the conversion factor as many times as it is powered

    Eg. 10cm
    ³ to m³
    10cm
    ³ x 1m/100cm x 1m/100cm x 1m/100cm

Then you can cancel out all the "cm" units since it corresponds to the power, and the product of the "m" unit would be cubed.


That is all there is to converting with more than one step!! Make sure to memorize your SI prefixes and conversion factor chart to help you with your conversions!

P.S: We will have a quiz next week about conversions and scientific notations, so be sure to memorize your chart! 





I hope that all this math isn't hurting your head! :P Goodluck!

(Today's entry by Grace Zhao)

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