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Course: MATH 1513, Fall 2011
School: Oklahoma State
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Word Count: 751

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R.2 Integer Section Exponents, Scientific Notation, Order of Operations W hen you see a term like x7 , x is called the base and 7 is called the exponent or power. 1. W hen the exponent is a positive integer (like 7 is), the term has a simple meaning: x7 x x x x x x x 7 factors 2. When the exponent is zero and the base is not zero, then x0 1. Similarly, 30 1, 0 1, 4.20 0 , etc. Notice we said that the base...

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R.2 Integer Section Exponents, Scientific Notation, Order of Operations W hen you see a term like x7 , x is called the base and 7 is called the exponent or power. 1. W hen the exponent is a positive integer (like 7 is), the term has a simple meaning: x7 x x x x x x x 7 factors 2. When the exponent is zero and the base is not zero, then x0 1. Similarly, 30 1, 0 1, 4.20 0 , etc. Notice we said that the base is not zero, this is because 00 is undefined. 3. When the exponent is a negative integer, a term like x 7 1 . Similarly, 1 3 x3 . 7 x x Simply stated, to get rid of a negative on an exponent, you move the term to the other side of the fraction bar (numerator to denominator or denominator to numerator) and remove the minus sign. For example: x3 y4 y4 x3 1 Math 1513 Sec R.2 Properties of Exponents Examples m n a a a a. x4 x6 x46 x10 mn 3 5 2 235 b. 4 4 4 4 9 a. x5 x95 x4 m a amn (a 0) n a x 6 b. z 5 z 65 z 11 1 z z11 32 2 n (am) a m a. (53) 5 mn b. ( y3)4 y a b m mm 12 1 y12 4 4 4 b. (3x2) 3 ( x2) 81x8 a. m am b 6 5 a. (2 y)3 23 y3 8 y3 (ab) a b 4 4 (b 0) b. 2 2 3 2 2 4 22 9 3x2 4 y3 3 4 34( x2)4 44( y3)4 81x8 256 y12 Math 1513 Sec R.2 Scientific Notation As the name suggests, this method for representing numbers is used in science e.g. physics and chemistry. It is a shorthand for representing very large numbers or very small numbers with lots of decimals. Heres how and why it works: If you multiply a number by a power of 10, the effect is to move the decimal to the right the same number of places as the exponent. For example: 1 2 3 14310 1430 , 14310 14300 , 14310 143000 If you multiply a number by a negative power of 10, the effect is to move the decimal to the left the same number of places as the exponent. For example: 1 2 3 14310 14.3, 1.43 14310 , 14310 .143 In scientific notation, we usually want to end up with one number to the left of the decimal. ___ ___ 126000 1.2610 0.0000945 9.4510 4 4 4.0510 6.1510 3 Math 1513 Sec R.2 More examples: 4 2 1. 1.210 2.410 5 2. 3.84 10 2 3.2 10 4 Math 1513 Sec R.2 Order of Operations W hen a mathematical term has several operations (exponentiation, multiplication, division, addition, subtraction) that must be performed, there are rules that determine the order in which the operations must be done. One way to remember this order, is to remember the initials P.E.M.D.A.S. This means do things in parentheses first, then the exponents, then multiplication, then division, then addition and finally subtraction. You may have heard of some of these ways to help remember PEMDAS or you may want to make up your own. People Eat More Donuts After School. Please Excuse M y Dear Aunt Sally. Purple Elk May Destroy A School. Pink Elephants Make Delicious Apple Sauce. 5 Math 1513 Sec R.2 Since we will be using the calculator to do many of our calculations, it is important to know the proper calculator language. Your calculator knows PEMDAS, but many times you have to help it by inputting additional notation so that it can do the arithmetic properly. Example: Compute: 23 4 7 3 You might be tempted to input this into your calculator as: That would be wrong. Entered that way, you are asking your calculator to multiply 2x3 then divide 4 by 7. Take those two results add them together and subtract 3. But in the original problem, the numerator 23 4 is to be divided by the denominator 7 4 . This would be: 23 4 6 4 2 0.666... 74 3 3 Probably the best and fastest way to work this problem in one step on the calculator would be: Make sure you understand why we needed to put parentheses around the numerator and denominator. 6 Math 1513 Sec R.2
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