Exponents and Scientific Notation: Understanding Bases, Exponents, and Rules, Study notes of Algebra

Download Exponents and Scientific Notation: Understanding Bases, Exponents, and Rules and more Study notes Algebra in PDF only on Docsity! a - |e <2, <ul \es Natuvc| wye\t TV asene rv Carne) Ceo\ Math 2303 Exponents and Scientific Notation We use exponents as a shorthand for multiplication. 35 5 5 5= ⋅ ⋅ In this example, the 5 is referred to as the base and the 3 is called the exponent. Generally speaking, nb b b b b b= ⋅ ⋅ ⋅ ⋅ ⋅⋯ n factors of b Example 1: Evaluate each: A. 32 B. 24 C. 100000001 D. 18 G. 08− H. ( )08− I. ( )05 3 93x y z− J. 16− K. 2 6 a a L. 2 5 5 4 2 x y x y M. ( ) ( ) 5 4 4 8 2 2 x y x y Scientific Notation Often scientists need to work with numbers that are very large or very small. Examples are 93,000,000 and 0.0000000008. All those zeros make these numbers hard to work with, so scientists developed scientific notation. 793,000,000 9.3 10= ∗ 100.0000000008 8.0 10−= ∗ Here are the rules: 1. Move the decimal point so that you have a number that is bigger than or equal to 1 and smaller than or equal to 10. 2. Did you need to move the decimal point to the left or to the right to accomplish step 1? 3. If you moved the decimal point to the left, you’ll multiply by a POSITIVE power of 10. If you moved the decimal point to the right, you’ll multiply by a NEGATIVE power of 10. 4. Multiply your number from step 1 by the power of 10 noted in step 3. Example 4: Write each using scientific notation. A. 23,000,000 B. 15,687,500,000,000 C. 0.0000000045 D. 0.000275 To write using decimal notation, here are the rules. 1. Look at the power to which 10 is raised. 2. If it’s positive, you’ll move the decimal point to the right the same number of places. You may have to add zeros. 3. If it’s negative, you’ll move the decimal point to the left the same number of places. You may have to add zeros. Example 5: Write each using decimal notation. A. 43.4 10−∗