1. Scientific Notation

2. The Long Way
4700
= 470 x 10
= 47 x 10 x 10
= 4.7 x 10 x 10 x 10
4.7 x 10 x 10 x 10 = 4.7 x (103)

3. Definitions 4.7 x (103) is called the standard form of 4700.
It is in scientific notation if the number at the start (4.7) lies between 1 and 10

4. Examples Write the following in scientific notation. 83000 = 8300 x 10
= 830 x 10 x 10
= 83 x 10 x 10 x 10
= 8.3 x 10x 10 x 10 x 10
= 8.3 x (104)
8.3 lies bewteen 1 and 10

5. Examples Write the following in scientific notation. 2. 631000
= x 10
= 6310 x 10 x 10
= 631 x 10 x 10 x 10
= 63.1 x 10 x 10 x 10 x 10
= 6.31 x 10 x 10 x 10 x 10 x 10
= 6.31 x (105)
6.31 lies bewteen 1 and 10

6. The Short Way Let’s look again at the examples 83000 = 8300 x 10
= 830 x 10 x 10
= 83 x 10 x 10 x 10
= 8.3 x 10x 10 x 10 x 10
= 8.3 x (104)
Changing to 8.3 meant moving the point 4 places

7. The Short Way Let’s look again at the examples 631000 = 63100 x 10
= 6310 x 10 x 10
= 631 x 10 x 10 x 10
= 63.1 x 10x 10 x 10 x 10
= 6.31 x 10 x 10 x 10 x 10 x 10
= 6.31 x (105)
Changing to 6.31 meant moving the point 5 places

8. Examples
Write in scientific notation.
29000
3300
987000
50000
701000

9. Examples Write in scientific notation. 29000 = 2.9 x 104

10. Example Convert from scientific notation to number form 8.3 x (104)
= 8.3 x 10 x 10 x 10 x 10
= 83 x 10 x 10 x 10
= 830 x 10 x 10
= 8300 x 10
= 83000

11. Example Convert from scientific notation to number form 6.31 x (105)
= 6.31 x 10 x 10 x 10 x 10 x 10
= 63.1 x 10 x 10 x 10 x 10
= 631 x 10 x 10 x 10
= 6310 x 10 x 10
= x 10 =

12. The Short Way Let’s look again at the examples 1. 8.3 x (104)
= 8.3 x 10 x 10 x 10 x 10
= 83 x 10 x 10 x 10
= 830 x 10 x 10
= 8300 x 10
= 83000
Changing 8.3 to meant moving the point 4 places to the right

13. The Short Way 1. 6.31 x (105) = 6.31 x 10 x 10 x 10 x 10 x 10=
Changing to 6.31 meant moving the point 5 places to the right

14. Examples Write in number form. 7.4 x 103 = 1.3 x 106 = 5.51 x 104 =

15. Examples Write in number form. 7.4 x 103 = 7400 1.3 x 106 = 1300000