PPT-Exponential and Scientific Notation

Power Exponential Notation A short hand of writing a number with out changing its Value It only changes the way it looks   X10 x10 Number gets larger . Consider the coordinate system illustrated in Figure 1 Instead of using the typical axis labels and we use and or 1 The corresponding unit basis vectors are then and or 1 The basis vectors and have the following properties 1 1 0 2 Figu By: Jenny Erickson. Adding in Scientific Notation. and. Subtracting in Scientific Notation. Adding and Subtracting…. The important thing to remember about adding or subtracting is that the exponents must be the same! . Exponential Function. f(x) = a. x. . for any positive number . a. other than one.. Examples. What are the domain and range of. . y = 2(3. x. ) – 4?. What are the. roots of . 0 =5 – 2.5. x. ?. Objectives. Express numbers in scientific notation.. Convert from standard form to scientific notation.. Convert from scientific notation to standard form.. Add, Subtract, Multiply, and Divide with scientific notation.. Scientific Notation Intro. Scientific Notation. Consists of two parts. 1. mantissa. The full size number that comes before x 10. 2. characteristic. The exponent that comes after x 10 and is superscript. Multiplying Numbers in Scientific Notation. Multiply the decimal numbers together.. Add the exponents to get the power of 10. . General formula. : . . (N X 10. x. ) (M X 10. y. ) = (N) (M) X 10. Evaluating Rational & Irrational Exponents. Graphing Exponential Functions . f(x) = a. x. Equations with . x. and . y. Interchanged. Applications of Exponential Functions. Use calculators to calculate graphing points. Section 3-1. The . exponential function f. with base . a. is defined by. . f. (. x. ) = . a. x. where . a. > 0, . a. .  1, and . x. is any real number.. For instance, . . f. (. x. ) = 3. Date: ______________. Warm-Up. Rewrite each percent as a decimal.. 1.) 8% 2.) 2.4% 3.) 0.01%. 0.08 0.024 0.0001. Evaluate each expression for x = 3.. 4.) 2. x. 5.) 50(3). x. 6.) 2. Exponential Growth. Exponential growth. occurs when an quantity increases by the same rate . r. in each period . t. . When this happens, the value of the quantity at any given time can be calculated as a function of the rate and the original amount. . Notation. Essentials questions. : How do you add, subtract, multiply, and divide using scientific notation?. Unit 1-3. Operations with Scientific. Notation. Quick review. Product rule . Quotient rule. REALLY, REALLY . BIG . OR. . REALLY, REALLY . SMALL. . NUMBERS.. Mathematicians . are Lazy!!!. They decided that by using powers of 10, they can create short versions of long numbers.. Rules for Scientific Notation. 210,000,000,000,000,000,000,000 miles. (22 zeros). This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.. Scientific Notation. A number is expressed in scientific notation when it is in the form. 4. 3. 2. 1. 0. In addition to 3, student will be able to go above and beyond by applying what they know about working with . integer . exponents..  .  .  .  .  . The student will be able to work with .