1. Algebra 1
Section 8.3

2. Scientific Notation Estimated number of atoms in a 154 lb human body:
7,000,000,000,000,000,000,000,000,000
Mass of an electron: kg

3. Definition
A number is written in scientific notation when it is expressed as a product in the form a × 10n, where 1 ≤ a < 10.

4. Scientific Notation
A number is written in scientific notation when it is expressed as a product in the form a × 10n, where 1 ≤ a < 10.

5. Since the decimal point moves six places to the left, we have
Scientific Notation
4,200,000
Since the decimal point moves six places to the left, we have
4.2 × 106

6. Since the decimal point moves five places to the right, we have
Scientific Notation
Since the decimal point moves five places to the right, we have
6.7 × 10-5

7. Move the decimal point four places to the left.
Example 1a
29,500
Move the decimal point four places to the left.
2.95 × 104

8. Move the decimal point eight places to the right.
Example 1b
Move the decimal point eight places to the right.
4.3 × 10-8

9. Example 2a
2.1 × 105
To express in standard notation, move the decimal point five places to the right.
210,000

10. Example 2b
6.8 × 10-6
To express in standard notation, move the decimal point six places to the left.

11. Scientific Notation
Products, powers, and quotients can all be calculated in scientific notation.
Be sure to write the result of such calculations in correct scientific notation.

12. Example 3a (7.5 × 10-5)(2 × 103) = (7.5 × 2)(10-5 × 103) = 15 × 10-2
But 15 is not between 1 and 10!
= (1.5 × 101) × 10-2
= 1.5 × 10-1

13. Example 3b
(1.2 × 10-4)2
= 1.22 × (10-4)2
= 1.44 × 10-8

14. Example 3c
(2.4 × 107) ÷ (6 × 102)
2.4 × 107
6 × 102
2.4 6
107
102
= ×
= 0.4 × 105
= (4 × 10-1) × 105
= 4 × 104

15. Scientific Notation
Before adding or subtracting numbers in scientific notation, make sure that both numbers are expressed using the same power of ten.

16. These powers of ten are the same.
Example 4a
(2.3 × 106) + (5 × 106)
These powers of ten are the same.
= ( ) × 106
= 7.3 × 106

17. The powers of ten are not the same.
Example 4b
(5.4 × 105) – (4.7 × 104)
The powers of ten are not the same.
= (5.4 × 105) – (0.47 × 105)
= (5.4 – 0.47) × 105
= 4.93 × 105

18. Metric Prefixes Prefix tera (T) giga (G) mega (M) kilo (K or k)
milli (m)
micro (μ)
nano (n)
10n
1012
109
106
103
10-3
10-6
10-9
Value
trillion
billion
million
thousand
thousandth
millionth
billionth

19. Example 5a (6 × 1023) = (0.6 × 1024) (6 × 1024) – (0.6 × 1024)
= 5.4 × 1024 kg

20. Example 5a
Earth is about 5.4 × 1024 kg more massive than Mars.

21. Example 5b (2 × 1027) ÷ (6 × 1024) 2 × 1027 kg 6 × 1024 kg 1 3 1027
= ×
= 0.3 × 103
≈ (3 × 10-1) × 103
= 3 × 102

22. Example 5b
Jupiter is about 300 times more massive than Earth.

23. Homework: pp