Chemistry 11: Scientific Notation, even more Uniting Rates.

Today in chemistry class we've learned about scientific notations and more uniting rates.

So, what is scientific notation?  Does it benefit us?  How?
Notice when you're solving math problems such as 125+521, you probably won't need to use scientific notation, you don't even need to use cauculator I believe.  But, since you're in a science class, you probably will meet such problems that encouters a huge quantities of ZERO.  In that kind of situation, scientific notation makes it easier for us to solve this kind of problems!  Scientific notation makes it simple to express very large and very small numbers using powers of 10 and to perform cauculations with these numbers.  Thus, scientific notation has helped advanced knowledge and has led to practical uses of this knowledge through technical development or in science.

Here is an example:
Ex. Express 25100000000 into scientific notation
       As you can see the number has quite a lot of ZEROs.  But we can use scientific notation to get rid of those ZEROs.
       1.locate the decimal points.  　25100000000.← 。
       2.and move the decimal points either left or right to make the number > 1 but <10.
                                                                       ←　　→                   = 2.5100000000
       3.count the number of places the decimal has moved.       2.5100000000   x   10
                                                                                                           10987654321 
       4.then place a x 10 beside the number, and whatever the number of places the decimal points was moved is the same as exponent.                                  ↑ 10 decimal places was moved
                                                                               2.5100000000 x 10^10
       5.See?!  After this procedure we've made 25100000000 a lot more easier to read!


Even more uniting rates.
     As we've learned before, 1km = 1000 m,   1m = 100cm.  But what if you receive such questions like 1m^2 =  ______ cm^2 ,  or  1m^3 = ______ cm^3 ?  Challenging, eh?
Let's take a look at this question: Convert 1m^2 to cm^2
                          we all know 1m = 100cm, now think about it, 10^2 = _____?  Yes, it's 10 x 10, therefore, it's the same meaning to cm^2, so what is 100 x 100?  It's 10000, so the answer to that question is 1m^2 = 10000 cm^2.  And now we can use the same idea to solve any kind of question like this.  
     For example:
                  Convert 8.1 m^3 to km^3.               1 km = 1000 m  → 10^3 m
                                                                             1 km^3 = 10^3 x 3 = 10^9 m^3   
                                      8.1 m^3  x  1 km^3      =   8.1 x 10^-9 km^3
                                                         10^9 m^3
                                                              ↑
                                                            flip it

                                                                                                                                  Leif Tung