University:
Montgomery College
Course:
CHEM 131: Principles of Chemistry I
Academic year:

2020
Views:

240

Pages:

2
Author:

Raina Flores

Scientific (Exponential) Notation The numbers used in chemistry are often either extremely large or extremely small. Such numbers are conveniently expressed in the form of scientific notation. N × 10n 1≤ N < 10 n is an exponent of 10 6 = 3.2 ×as106.022 × 10×× 10× 3.2 × 10 The Avogadro number is written 1023.10× 10× 10 = 3,200,000 Positive Exponents: Each time the Negative Exponents: Each time the decimal place is moved once place to the right, the exponent is decreased by one. decimal place is moved once place to the left, the exponent is increased by one. 5237.3 × 100 = 523.73 × 101 523.73 × 101 = 52.373 × 102 52.373 × 102 = 5.2373 × 103 = 5.2373 ×10×10×10 0.00386 × 100 = 0.0386 × 10-1 0.0386 × 10-1= 0.386 × 10-2 0.386 × 10-2 = 3.86 × 10-3 3.86 10 ×10 ×10 Operations with Scientific Notation Addition and Subtraction: In order to add or subtract numbers expressed in scientific notation, the powers of 10 must be the same. Not equal 3 Equal 4 4 (3.2 × 10 ) + (7.23 × 10 ) = (0.32 × 10 ) + (7.23 × 104) = (0.32 + 7.23) × 104 = 7.55 × 104 The decimal is moved to the left to increase the exponent. Multiplication: When numbers in scientific notation are multiplied, only the number is multiplied. The exponents are added. (5.4 × 102)(2.1 × 103) = (5.4)(2.1) × 102+3 = 11 × 105 = 1.1 × 106 Division: When numbers in scientific notation are divided, only the number is divided. The exponents are subtracted. 3.2 ×105 6.5 × 10 2 = 3,2 6.5 × 105-2 = 0.49 × 102 = 4.9 × 102 Practice Problems 1. Convert the following numbers into scientific notation. a) 923 _______________________________ b) 0.00425 _______________________________ c) 4523000 _______________________________ d) 0.94300 _______________________________ e) 92.03 _______________________________ f) _______________________________ 7.80 2. Convert the following numbers into standard notation. a) 3.92400 x 105 _______________________________ b) 9.2 x 106 _______________________________ c) 4.391 x 10 -3 d) 6.825 x 10 e) 8.36 x 101 f) 2.46 x 10 -4 -5 _______________________________ _______________________________ _______________________________ _______________________________ 3. Perform the following operations and express the answers in scientific notation. a) (1.2 × 105) + (5.35 × 106) b) (6.91 × 10-2) + (2.4 x 10-3) c) (3.67 × 102) - (1.6 × 101) d) (3.378 × 10-3) - (4.97 × 10-5) e) (5.98 × 1012) × (2.77 × 10-5) f) (6.0 × 103) × (1.5 × 10-2) g) (7.8 x 103) ÷ (1.2 x 104) h) (6.48 x 105) ÷ [(2.4 x 104) (1.8 x 10-2)] References: Tro, Chemistry: A Molecular Approach, 2nd ed., Pearson Brown/LeMay/Bursten, Chemistry: The Central Science, 12th ed., Pearson 1. a) 9.23 x 102; b) 4.25 x 10-3; c) 4.523 x 106; d) 9.4300 x 10-1; e) 9.203 x 101; f) 7.80 x 100 2. a) 392400; b) 9200000; c) 0.004391; d) 0.0006825; e) 83.6; f) 0.0000246 3. a) 5.47 × 106; b) 7.15 × 10-2; c) 3.51 × 10-2; d) 3.328 x 10-3; e) 1.66 x 108; f) 9.0 × 101 g) 6.5 × 10-1; h) 1.5 × 102 Answers