Algebra 1 Section 8.3

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: 0.0000000000000000000000000000009109 kg

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

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.

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

Since the decimal point moves five places to the right, we have Scientific Notation 0.000067 Since the decimal point moves five places to the right, we have 6.7 × 10-5

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

Move the decimal point eight places to the right. Example 1b 0.000000043 Move the decimal point eight places to the right. 4.3 × 10-8

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

Example 2b 6.8 × 10-6 To express in standard notation, move the decimal point six places to the left. 0.0000068

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.

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

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

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

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

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

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

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

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

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

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

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

Homework: pp. 341-343