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.

3. Why use scientific notation?
For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.
Numbers expressed in scientific notation can be used in a computation with far greater ease.

4. Proper Scientific Notation consists of two parts:
A number between 1 and
A power of 10
N x 10x

5. Are these in proper scientific notation form?
x 109
4.1 x 104
x 10-3
x 1029
9.002 x 100
x 102 NO
YES NO
YES
YES NO

6. Changing standard form to scientific notation.

7. To change standard form to scientific notation…
Place the decimal point so that there is one non-zero digit to the left of the decimal point.
Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

8. Continued…
If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

9. Example 1 Given: 289,800,000 Use: 2.898 (moved 8 places)
Answer: x 108

10. Example 2 Given: 0.000567 Use: 5.67 (moved 4 places)
Answer: 5.67 x 10-4

11. Practice
378000 b c d e
3.78 x 105
9.340 x 10-3
9.83 x 10-7
x 100
x 101

12. Changing scientific notation to standard form.

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

14. Example 3
Given: x 106
Answer: 5,093,000 (moved 6 places to the right)

15. Example 4
Given: x 10-4
Answer: (moved 4 places to the left)

16. Practice
a x 105
b x 10-4
c x 102
149300

17. Doing Math with Numbers in Scientific Notation
Addition/Subtraction
Convert small number into same power of ten as larger
Carry out operation
Adjust to proper form if needed

18. Example 3.2 x 103 + 5.7 x 104 Step #1 Change smaller to larger
Step #2 Carry out operation
.32 x x 104 = 6.02 x 104
Step #3 Adjust if needed
Not needed

19. Doing Math with Numbers in Scientific Notation
Mulitplication
Multiply leading numbers
Add exponents
Adjust to proper form if needed

20. Example 3.2 x 103 times 5.7 x 104 Step #1 Multiply leading numbers
Step #2 Add exponents
= 107
Step #3 Adjust if needed
18 x 107  1.8 x 108

21. Doing Math with Numbers in Scientific Notation
Division
Divide leading numbers
Subtract exponents (N-D)
Adjust to proper form if needed

22. Example 3.2 x 103 divided by 5.7 x 104 Step #1 Divide leading numbers
3.2 / 5.7 = 0.56
Step #2 Subtract exponents
= 10-1
Step #3 Adjust if needed
0.56 x 10-1  5.6 x 10-2