1. Making Your Life Easier
Scientific Notation
Making Your Life Easier

2. My calculator can’t even handle this many digits!
Example Problem
Calculate the force of the sun on the earth:
Decimal Notation (Normal)
My calculator can’t even handle this many digits!

3. Notes: Scientific Notation
· means multiply
Example: 340 = 3.4 · 102
M n

4. Notes: Decimal Notation  Scientific Notation
Example:
658,000.
Example:
658,000
Note: if no decimal point is written it automatically goes at the end (right) of the number

5. Notes: Decimal Notation  Scientific Notation
Example:
658,000.
Example:
6.58,000.

6. Notes: Decimal Notation  Scientific Notation
Example:
6.58,000.
Example:
658,000
n = 5

7. Notes: Decimal Notation  Scientific Notation
Example:
658,000
Example:
6.58,000.
n = 5
Note: n is positive since 658,000 is bigger than 1

8. Notes: Decimal Notation  Scientific Notation
Example:
658,000 = 6.58 ·105

9. Notes: Scientific Notation  Decimal Notation
Example:
7.04 ·10-3

10. Notes: Scientific Notation  Decimal Notation
Example:
7.04 ·10-3

11. Notes: Scientific Notation  Decimal Notation
Example:
7.04 ·10-3

12. Notes: Scientific Notation  Decimal Notation
Example:
·10-3

13. Notes: Scientific Notation  Decimal Notation
Example:
·10 -3

14. Notes: Scientific Notation  Decimal Notation
Example:
7.04 ·10-3 = 0.007,04
Added so you notice the decimal point

15. My calculator can’t even handle this many digits!
Example Problem
Calculate the force of the sun on the earth:
Decimal Notation (Normal)
My calculator can’t even handle this many digits!

16. Much easier! Your calculator can do this for you.
Example Problem
Calculate the force of the sun on the earth:
Scientific Notation
Much easier! Your calculator can do this for you.

17. Notes:

18. Your Turn! Convert to Scientific Notation: 55,601

19. Your Turn! Convert to Scientific Notation: 55,601
55,601 = 5.560,1 ·104
2. Convert to Scientific Notation: 30,800,000
30,800,000 = 3.08 ·107
3. Convert to Scientific Notation:
0.034 = 3.4 ·10-2
Convert to Scientific Notation: 0.005,000,702
0.005,000,702 = 5.000,702 ·10-3

20. Your Turn! 5. Convert to Decimal Notation: 6.0 ·104

21. Your Turn! 5. Convert to Decimal Notation: 6.0 ·104 6.0 ·104 = 60,000
9.05 ·10-11= 0.000,000,000,090,5
7. Convert to Decimal Notation: ·10-1
8.820 ·10-1= 0.882,0
8. Convert to Decimal Notation: 4.532,1 ·1013
4.532,1 ·1013= 45,321,000,000,000