1. Scientific Notation

2. What is scientific Notation?
Scientific notation is a way of expressing really big numbers or really small numbers.
It is most often used in “scientific” calculations where the analysis must be very precise.
Numbers expressed in scientific notation can be used in a calculation with far greater ease.

3. Scientific notation = two parts:
A number between 1 and 10 possibly followed by a decimal point and more numbers
1,2,3,4,5,6,7,8,or 9
A power of 10
N x 10z

4. How to convert into Scientific Notation
Rewrite all the digits as a number with only one digit in front of the decimal point and the rest of the digits after it.
Count the number of places you moved the decimal point
If you had to move the decimal point to the left, the exponent of the power of ten is positive.
If you had to move the decimal point to the right, the exponent of the power of ten is negative.

5. Examples Given: 289,800,000 Use: 2.898 (moved 8 places)
Answer: x 108
Given:
Use: 5.67 (moved 4 places)
Answer: 5.67 x 10-4

6. Practice Problems - Converting to Scientific Notation
378000
1.9284
34.903
783920
3.78 x 105
9.34 x 10-3
8.3 x 10-7
x 10 0
x 101
x 105

7. To change scientific notation to standard form…
Simply move the decimal point to the right for positive exponent of 10.
Move the decimal point to the left for negative exponent of 10.
(Use zeros to fill in places.)

8. Examples Given: 5.093 x 106 Answer: 5,093,000 Given: 1.976 x 10-4
(moved 6 places to the right)
Given: x 10-4
Answer:
(moved 4 places to the left)

9. Practice Problems - Converting back to Standard Form
1.493 x 105
2.908 x 10-4
x 102
1.333 x 10-1
x 107
2.345 x 104
149300
0.1333
23450