1. Scientific Notation Significant Digits
Physics
Mr. Villa

2. In any measurement, the number of significant figures is critical.
The number of significant figures in a result is simply the number of figures that are known with some degree of reliability. 
The number 13.2 is said to have 3 significant figures. The number is said to have 4 significant figures.

3. Significant Figures
Rules for deciding the number of significant figures in a measured quantity:
(1) All nonzero digits are significant:
1.234 g has 4 significant figures, 1.2 g has 2 significant figures.
(2) Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures, 3.07 mL has 3 significant figures.

4. Significant Figures
(3) Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point:
0.001  has only 1 significant figure, g has 2 significant figures.
(4) Trailing zeroes that are also to the right of a decimal point in a number are significant:
mL has 3 significant figures, 0.20 g has 2 significant figures.

5. Practice Significant Figures
 1.05  =    
  =  
 4.566 =
4.    =        
5.   =  
 845.6 =
7.   =      
8.   =      
9.   =

6. Scientific Notation A x10b Where, A is a real number b is an integer
Scientific notation is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. In scientific notation all numbers are written like this:
Where,
A is a real number
b is an integer
Example
A x10b
Ordinary decimal notation
Scientific notation (normalized)
200
2×10^2
4,000
4×10^3
4,880,000,000
4.88×10^9
9.1×10^−9

7. Scientific notation Examples
500 in scientific notation is written like this
5.0x102
The exponent 2 that is on top of the 10 is because you moved the decimal 2 spots. If the number does not have a decimal like 500 then always put an imaginary decimal at the end.

8. Scientific Notation
Big Numbers (positive exponent): The exponent refers to the number of zeros that follow the 1. Moving the decimal to the left example: x10^3 101 = 10 = 10x1 102 = 100 = 10 x = 1,000 = 10x10x = 10,000 = 10x10x10x10 Small Numbers (negative exponent) Negative notations indicate numbers smaller than 1. Moving the decimal to the right example: x10^ = 1/10 = = 1/100 = = 1/1,000 = .001

9. Standard Form
If a number is already in scientific notation then we can change it back to standard form.
Example:
7.8x 104 would be written 78,000 because we moved the decimal place 4 to the right because of the 4 exponent on top of the 10.
7.8x10-4 would be written because we moved the decimal place 4 to the left because of the negative 4 on top of the 10.

10. Convert these numbers to standard notation or scientific notation
Lets Practice!
Convert these numbers to standard notation or scientific notation
6.17 x104
2.07 x10-3
.00098
61700
00207
9.8 x10-4
1.397 x108