What is the value of the expression ? Express your answer in both scientific and standard notation.

Question

 

6 x 10 ^-4

________

 

2x 10³

Answer 1

There are two ways to evaluate expressions like this.

One way is to work out the scientific notation first, and then divide.

 6x10^-4       Neg exp mean move the decimal pt left

---------

 2x10³        Pos exp mean move the decimal pt right

 

 

 0.0006

---------  = 0.0000003

  2000

 

 

This method can become challenging as the exponents get larger, so I actually recommend a second method, which involves dividing with scientific notation:

 

 6x10^-4   We can break this up into "like terms"
---------
 2x10³ 

 

 

 6   x   10^-4   Now we'll divide each fraction

---      ------

 2   x   10³  The quotient rule tells us to subtract powers

 

 

3 x 10^-7, which is equivalent to 0.0000003, which is the same answer from above.