Scientific Notation

1. Math Notebook & Pencil Scientific Notation

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 Scientific Notation

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? Let’s Look at Our Example

4. Examples

5. The exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. Apositive exponent shows that the decimal point is shifted that number of places to the right. Anegative exponent shows that the decimal point is shifted that number of places to the left. As you can see…

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 107 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 = 102 Scientific notation, 124 is written as 1.24 × 102. Write 124 in scientific notation. 

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 Write in decimal notation:  3.6 × 1012

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. Write 0.000 000 000 043 6 in scientific notation.

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 Let’s Practice