University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

222

Pages:

1
Author:

perlesdesfees9ovd

Mini-Lecture 5.5 Negative Exponents and Scientific Notation Learning Objectives: 1. 2. 3. 4. Simplify expressions containing negative exponents. Use all the rules and definitions for exponents to simplify exponential expressions. Write numbers in scientific notation. Convert numbers from scientific notation to standard form. Examples: 1. Simplify each expression. Write each result using positive exponents only. x −4 a) 3−2 b) 8a −3 c) −3 d) 4 −2 + 40 y 2. Simplify each expression. Write each result using positive exponents only. ( 2x ) 4 a) a −6 i a −3 i a i a −2 ( ) (m ) m 2 m −4 e) −2 5 −2 b) 3 c) x15 ⎛ 3 xy 5 f) ⎜ 4 7 ⎜ 2x y ⎝ ⎞ ⎟⎟ ⎠ −3 (x −2 8 y ) −2 ⎛ 3a −3b −2 ⎞ g) ⎜ −2 −5 ⎟ ⎜ 6a b ⎟ ⎝ ⎠ d) 0 h) −6 x 2 y −3 −12 x5 y −6 ( −2 r −3 −2 )( s t −5t −4 3. Convert the following numbers in standard form to scientific form. a) 83,000 b) 1,250,000 c) 0.000154 d) 0.00000689 4. Convert the following numbers in scientific form to standard form. a) 1.03 x 106 b) 8.7 x 10-5 c) 6.003 x 1010 d) 2.02 x 10-3 Teaching Notes: • • • Many students move the numerical coefficient along with the variable. For example, in 1b) a 1 common incorrect answer is 8a-3 = 3 8a Overall, students need a lot of practice with these rules to master these objectives. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 1/9; 1b) 8/a3; 1c) y3/x4; 1d) 17/16; 2a) 1/a10; 2b) 8/x3; 2c) x4/y16; 2d) y3/2x3; 2e) m20; 2f) 8 x9 y 6 10 ; 2g) 1; 2h) 3 2 3 ; 3a) 8.3x104; 3b) 1.25x106; 3c) 1.54x10-4; 3d) 6.89x10-6; 4a) 1,030,000; 27 r s t 4b) 0.000087; 4c) 60,030,000,000; 4d) 0.00202 )