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Objective: To express and find the value of numbers using an exponent and a base 14.1 Introduction to Exponents Slide 2 3 + 3 + 3 + 3 How can we write the same expression using multiplication? Therefore, multiplication is simply_____ addition. Slide 3 Suppose we have repeated multiplication such as 3 x 3 x3 x3 How can we rewrite this in a more concise manner? Exponent is a shortcut for showing repeated multiplication. For example, 3 4 = 3 x 3 x 3 x 3 = 81 Slide 4 2727 Base: a numbers used as a factor Exponent: the number of times a base is used as a factor. Slide 5 Exponents, also called powers, are the number of times a base number is multiplied by itself. Exponent problems can be written in several different forms: 3rd power of five or 5 3 --------Exponential form 5 x 5 x 5 --------Expanded form 125 ------Standard form Slide 6 What does 2 4 mean? What is the base ? What is the exponent? Slide 7 Exponential Form Expanded Form Standard Form 10 3 1,000 3636 729 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 Slide 8 Is 2 4 the same as 4 x 2? Can you think of any number you can represent using exponential form? Slide 9 Write the following in word and expanded form: 5 2 6 3 20 4 1 5 Slide 10 The following rules apply to numbers with exponents of 0, 1, 2 and 3: Slide 11 When the base is 10 You always have _________ in the product. The number of zeros is the same as the exponent of 10. Slide 12 Powers of 10 6 x 10 3 7 x 10 2 8 x 10 0 4 x 10 1 Slide 13 Slide 14 Summary 1. Exponents 2. Base and Exponent 3. Forms of writing exponents 4. Rules for numbers with exponents of 0,1,2,and 3 5. Power of 10 Slide 15 Why Exponents? If you talk about SQUARE shaped areas, for example if you say "My room is twelve by twelve square feet", you're meaning your room is 12 feet x 12 feet, or 12 2 square feet. Another example is if you talk about extremely tiny or extremely big quantities. For example, the term 'nanometer' means 10 -9 meter. The prefix 'nano' means the number 10 -9 - an extremely small number. Or, within computer world you often see megabytes, gigabytes, terabytes. "Mega" means 10 6 or one million, "giga" means 10 9, and "tera" means 10 12. Or megahertz - million hertz. Slide 16 Scientific Notation Is the way that scientists easily handle very large or very small numbers. For example instead of writing : Speed of Light as (approximately) 300,000,000 m/s 3 x 10 8 Slide 17 Class work Txt Book Page 294 Q 16 to 21 without finding the value Q22, 24, 32, 33, 40, and 46 to 49 Pg 298 Q 9 to 13 Homework PW Pg 72 Q 1 to 6 without finding the value and Q 10,11, 14,15, 17