1. Chapter 3 Exponents, Factors, and Fractions

2. 3-1 to 3-2 Exponents, Orders of Operations, and Scientific Notation What You’ll Learn  To write numbers with exponents  To simplify expressions with exponents using orders of operations  To write numbers in scientific notation  To write numbers in standard form

3. Exponential Notation  An exponent is a number that represents how many times the base is used as a factor. For example, the number 8 with an exponent of 4 is equal to 8 x 8 x 8 x 8.  Base  Exponent

4. Exponential Notation  The most common error among students learning about exponents is multiplying the base number by the exponent. That is, many students will calculate 8 to the 3rd power as 8 x 3 = 24. The correct answer is 8 x 8 x 8 = 512.

5. Writing Expressions Using Exponents  Write using and exponent 3*3*3*3*3  3^5 11*11*11  11^3 5*5*5*5*5  5^5

6. Simplifying Powers with Negatives  -5^4 =? -1 * 5^4 -625  (-5)^4 = ? (-5)(-5)(-5)(-5) 625

7. Simplifying Using Order of Operations  The order of operations must be followed when working with grouping symbols and/or multiple step operations. The order of operations are as follows: 1. Perform operations within parentheses, braces, or brackets. 2. Perform operations with exponents. 3. Multiply and divide from left to right 4. Add and subtract from left to right

8. Simplify: 3^4*(7-2)^3  3^4*5^3  81*125  10,125  Do operations in Parenthesis  Find the values of the powers  Multiply

9. Scientific Notation  Scientific notation is a condensed way to write very large or small numbers without including each digit. Scientific notation is a number written as the product of a number between 1 and 10 and a power of 10.

10. Scientific Notation  To write a large number using scientific notation count the digits (from right to left) to be between 1 and 10. The amount of spaces counted will be the exponent of 10 represented by a power of 10.  123,000,000 can be written in scientific notation as 1.23 x 10 to the 8th power. To write a small number, count the digits from left to right. To undo scientific notation, move the decimal point the same number of places as the exponent in the power of ten.

11. Example 1:  Answer: 62,900,000 (move the decimal 7 places to the right) Example 2:  Answer: The missing exponent would be 4

12. Negative Exponents  Remember that a number in scientific notation is written as a product of two factors, one greater than or equal to 1 and less than 10, and the other a power of 10. To write a number between 0 and 1 in scientific notation, you can use a negative exponent.

13. Negative Exponents  Writing in Scientific Notation If the decimal point is moved to the right to make a number between 1 and 10, the number will have a negative exponent  Writing in Standard Form If the exponent is negative the decimal point must be moved to the left the given number of times

14. Negative Exponents  Example 3 Writing in Scientific Notation Write 0.0084 in Scientific Form  Move decimal point three places to the right  Since we went to the right the exponent will be a negative (-3)  8.4 x 10^-3  Example 4 Writing in Standard Form Write 3.52 x 10 ^ -5  Since the exponent is negative move to the left 5 places  0.0000325