1. Math Notebook & Pencil

2.  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 0.0000000056, we write 5.6 x 10 -9

3.  We can think of 5.6 x 10 -9 as the product of two numbers: 5.6 (the digit term) and 10 -9 (the exponential term).  What does “product” mean in math terms?

4. RuleExample of the Rule 10000 = 1 x 10 4 24327 = 2.4327 x 10 4 1000 = 1 x 10 3 7354 = 7.354 x 10 3 100 = 1 x 10 2 482 = 4.82 x 10 2 1 = 10 0 Anything to the zeroth power is 1 1/100 = 0.01 = 1 x 10 -2 0.053 = 5.3 x 10 -2 1/1000 = 0.001 = 1 x 10 -3 0.0078 = 7.8 x 10 -3 1/10000 = 0.0001 = 1 x 10 -4 0.00044 = 4.4 x 10 -4

5.  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.

6.  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,  46600000 = 4.66 x 10 7  This number only has 3 significant figures.

7.  The zeros are not significant; they are only holding a place.  As another example,0.00053 = 5.3 x 10 -4  This number has 2 significant figures. The zeros are only place holders.

8. 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.

9.  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

10.  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.

11.  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

12.  Write 23,000,000,000 in scientific notation  Write 0.00000000023 in scientific notation