1. Scientific Notation
Scientific notation is used when numbers are either very large or very small
Standard Notation
Scientific Notation
Measurement
300,000,000 m/sec
3.00×108 m/s
speed of light
 kg
×10−31 kg
mass of electron
 kg
1.6726×10−27 kg
mass of proton
 kg
5.9736×1024 kg
mass of Earth kg
7.53×10−10 kg
mass of a dust particle
 m (40 Mm)
4×107 m
circumference of Earth km
x1012 km
one light year

2. Scientific Notation is based on powers of the base number 10
The number 123,000,000,000 in scientific notation is written as:
𝟏.𝟐𝟑 𝒙 𝟏𝟎 𝟏𝟏
The first number, 1.23, is called the coefficient. It must be greater than or equal to 1 and less than 10.
The second number is called the base. It must always be 10 in scientific notation.
The number 11 is referred to as the exponent.

3. Converting from Standard Form to Scientific Notation
Place the decimal point to the right of the first non-zero digit.
Count the number of decimal places the decimal has "moved" from the original number.  This will be the exponent of the 10.
If the original number was less than 1, the exponent is negative;
If the original number was greater than 1, the exponent is positive.

4. Examples:
Given: (moved decimal point 6 decimal places)
Answer:  4.75 X 106
The original number was greater than 1 so the exponent is positive
Given: 
7.89 (moved decimal point 4 decimal places)
Answer:  7.89 X 10-4
The original number was less than 1 so the exponent is negative

5. Converting from Scientific Notation to Standard Form
Move the decimal point to the right for positive exponents of 10. The exponent tells you how many places to move. 
Move the decimal point to the left for negative exponents of 10. The exponent tells you how many places to move.

6. Examples:
Given:  x 10-8
Negative exponents move decimal to the left
Answer:    
Given:  x 103
Positive exponents move decimal to the right
Answer:  5024

7. Try working on Practice Questions …
Scientific Notation
Ex) Convert the following to scientific notation:
(a) = ______________________
(b) = ____________________
5.3 x 10-5
4.0 x 107
Try working on Practice Questions …
Express the following numbers in scientific notation:
= _________________________
= _________________________
58.23 = _________________________
= _________________________
12452 = _________________________
1.003 x 1012
3.998 x 10-10
5.823 x 101
2.038 x 10-1
x 104

8. For the following use the exponent button on your calculator
2. Express the following numbers to decimal notation:
1.77 x 107 = ________________________
2.552 x 10-9 = _________________________
1.18 x 103 = _________________________
4.44 x 10-1 = _________________________
1.399 x 100 = _________________________
1180
0.444
1.399
For the following use the exponent button on your calculator
EXP, E, EE, x10x
3. Express the results of the following operations in scientific notation:
1.39 x x 10-4 = _________________________
1.17 x x 102 = _________________________
(1.81 x 10-3) (1.06 x 1020) = _________________________
(5.77 x 10-4)  (1.71 x 10-11) = _________________________
1.42 x 10-2
1.13 x 104
1.92 x 1017
3.37 x 107