Math Notebook & Pencil

 Scientific notation is the way that scientists easily handle very large numbers or very small numbers. You will always use a number times 10 to a power.  For example, instead of writing , we write 5.6 x 10 -9

 We can think of 5.6 x as the product of two numbers: 5.6 (the digit term) and (the exponential term).  What does “product” mean in math terms?

RuleExample of the Rule = 1 x = x = 1 x = x = 1 x = 4.82 x = 10 0 Anything to the zeroth power is 1 1/100 = 0.01 = 1 x = 5.3 x /1000 = = 1 x = 7.8 x /10000 = = 1 x = 4.4 x 10 -4

 The exponent of 10 is the number of places the decimal point must be shifted to give the number in long form.  A positive exponent shows that the decimal point is shifted that number of places to the right.  A negative exponent shows that the decimal point is shifted that number of places to the left.

 In scientific notation, the digit term indicates the number of significant figures in the number.  The exponential term only places the decimal point. As an example,  = 4.66 x 10 7  This number only has 3 significant figures.

 The zeros are not significant; they are only holding a place.  As another example, = 5.3 x  This number has 2 significant figures. The zeros are only place holders.

To convert this to scientific notation, You first write "1.24". This is not the same number, but (1.24)(100) = 124  100 = 10 2  Scientific notation, 124 is written as 1.24 × 10 2.

 Since the exponent on 10 is positive, You know they are looking for a LARGE number  You’ll need to move the decimal point to the right, in order to make the number LARGER.  Since the exponent on 10 is "12", You’ll need to move the decimal point twelve places over.  First, you’ll move the decimal point twelve places over.  Make little loops when you count off the places, to keep track. Fill in the loops with zeros

 The number we are concerned about is the three digit number 436.  So I will count how many places the decimal point has to move to get from where it is now to where it needs to be; between the 4 and the 3.

 Then the power on 10 has to be –11: "eleven", because that's how many places the decimal point needs to be moved, and "negative", because I'm dealing with a SMALL number.  Scientific notation, the number is written as

 Write 23,000,000,000 in scientific notation  Write in scientific notation