This document discusses scientific notation and how to convert between standard and scientific notation. It explains that scientific notation involves writing a number as the product of a number between 1 and 10 and a power of 10. To convert a number to scientific notation, you move the decimal point of the number until it is between 1 and 10, and the power of 10 indicates how many places the decimal is moved. Several examples are provided of converting numbers between standard and scientific notation forms.

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.
1. 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. 361000
= 36100 x 10
= 3610 x 10 x 10
= 361 x 10 x 10 x 10
= 36.1 x 10 x 10 x 10 x 10
= 3.61 x 10 x 10 x 10 x 10 x 10
= 3.61 x (105
)
3.61 lies bewteen 1 and 10

6. The Short Way
Let’s look again at the examples
1. 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 83000 to 8.3 meant
moving the point 4 places

7. The Short Way
Let’s look again at the examples
1. 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 631000 to 6.31 meant
moving the point 5 places

8. Examples
Write in scientific notation.
1. 29000
2. 3300
3. 987000
4. 50000
5. 701000

9. Examples
Write in scientific notation.
1. 29000 = 2.9 x 104
2. 3300 = 3.3 x 103
3. 987000 = 9.87 x 105
4. 50000 = 5 x 104
5. 701000 = 7.01 x 105

10. Example
Convert form scientific notation to number form
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

11. Example
Convert form scientific notation to number form
1. 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
= 63100 x 10
= 631000

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 83000 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
= 63.1 x 10 x 10 x 10 x 10
= 631 x 10 x 10 x 10
= 6310 x 10 x 10
= 63100 x 10
= 631000
Changing 631000 to 6.31 meant
moving the point 5 places to
the right

14. Examples
Write in number form.
1. 7.4 x 103 =
2. 1.3 x 106 =
3. 5.51 x 104 =
4. 3 x 101 =
5. 4.27 x 107 =

15. Examples
Write in number form.
1. 7.4 x 103
= 7400
2. 1.3 x 106
= 1300000
3. 5.51 x 104
= 55100
4. 3 x 101
= 30
5. 4.27 x 107
= 42700000

16. Textbook pg 19 Ex 1.11
Questions 1 - 5