ࡱ> 685y@ ETbjbjFF "X,,06666666J R!TJ1!V$$$$U%U%U%0000000$R2R4196%3%"U%%%166$$+V12(2(2(% 6$6$02(%02(2(V+0@660$! ~Q &k0 0l101w00<5'"<50JJ6666<560PU%i%2(w% %wU%U%U%11JJ ("JJ EXPONENTS, SQUARE ROOTS AND RADICALS INSTRUCTION SHEET A. Exponents - An exponent is a shorthand way of writing multiplication of the same number 10 - 10 is the base number It is read: Ten to the third power 3 is the exponent It means: 10 x 10 x 10 (The exponent tells how many times a number should be multiplied by itself) Example 1: 44 = 4 x 4 x 4 x 4 = 256 Example 2: 8 x 8 x 8 x 8 x 8 x 8 = 86 Example 3: 5 + 2 = (5 x 5 x 5) + (2 x 2) = 125 + 4 = 129 Example 4: 55 = 3125 54 = 625 53 = 125 52 = 25 51 = 5 50 = 1 any number to the zero power equals 1 B. Square roots - When a number is a product of 2 identical factors, then either factor is called a square root. A root is the inverse of the exponent. Example 1:  EMBED Equation.3  = 2 Example 2:  EMBED Equation.3 = 10 These are all called perfect squares because the Example 3:  EMBED Equation.3 = 13 square root is a whole number. Example 4:  EMBED Equation.3  =  EMBED Equation.3  When a number will not result in a perfect square, it can be estimated or a calculator with the  EMBED Equation.3  (square root) function can be used. Example 5:  EMBED Equation.3  H" 6.3 because,  EMBED Equation.3  = 6 and  EMBED Equation.3  = 7, since 40 is closer to 36, the square root will be closer to 6. On a calculator using the  EMBED Equation.3  key, the rounded answer is 6.325. Sometimes you may be asked to find a root higher than 2. Example 1:  EMBED Equation.3 = 4 because if you multiply 4 by itself three times, the result is 64. Example 2:  EMBED Equation.3 = 3 because if you multiply 3 by itself 7 times, the result is 2187 Exponents, Square Roots and Radicals Worksheet Find the value of each expression. 38 46 73 84 92 Write each product in exponent form. 6 x 6 x 6 x 6 x 6 5 x 5 x 5 x 5 7 x 7 x 7 x 7 x 7 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 11 x 11 x 11 12 x 12 Find the value of each expression. (Hint: Remember to use proper order of operations.) 34 + 26 = 72 x 84 = 5 + 70 = 65 19 = 4 + 18 3 - 3 x (8 - 6) = Which of the expressions listed below will result in a perfect square?  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Find the square root of the following:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Find the required root of the following:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Solve the following expressions: 5 EMBED Equation.3  12( EMBED Equation.3 )2 2  EMBED Equation.3  -5 EMBED Equation.3  3 EMBED Equation.3 + 9 EMBED Equation.3   3 EMBED Equation.3  SCIENTIFIC NOTATION INSTRUCTION SHEET To write long numbers, it is typical to use scientific notation, a system based on the powers of 10. 100 = 1 101 = 10 10-1 = .1 102 = 100 10-2 = .01 103 = 1000 in the same way 10-3 = .001 104 = 10000 10-4 = .0001 105 = 100000 10-5 = .00001 106 = 1000000 10-6 = .000001 To write 435,000,000 in scientific notation Turn the number into a number between 1 an 10 4.35000000 Multiply it by a power of ten to simplify 4.35 x 108 The power is determined by the number of places the decimal is moved to return the number to its original designation If I move the decimal 8 places to the right (positive direction), I will end up with 435,000,000 my original number Example 1: 260,000 equals 2.6 x 105 Example 2: 10, 400,000 equals 1.04 x 107 Example 3: .0000042 equals 4.2 x 10-6 Example 4: .000204 equals 2.04 x 10-4 We can also turn a number notated scientifically into a decimal number by reversing this process If I have 8.7 x 109 I can convert this to decimal by simply moving the decimal point 9 places to the right (positive exponent) x 109 = 8,700,000,000 If I have 5.4 x 10-7 I can convert this to decimal by simply moving the decimal point 7 places to the left (negative exponent) x 10-7 = .00000054 Example 1: 6.3 x 104 = 63000 Example 2: 9.32 x 10-3 = .00932 Example 3: 3.04 x 10-8 = .0000000304 Example 4: 5.003 x 106 = 5,003,000 Scientific Notation Practice Write in ordinary notation: 1. 2.54 101 2. 6.19 103 3. 8.07 108 4. 1.05 1010 5. 4.64 10-1 6. 7.04 10-3 7. 3.02 10-5 8. 4.16 10-8 9. 1.29 100 10. 5.02 100 Write in scientific notation: 11. 575 12. 87,400 13. 2,010,000 14. 603,000,000,000 15. 0.643 16. 0.000802 17. 0.00000404 18. 0.000000000269 19. 2.34 20. 1.00 WORD PROBLEMS PRACTICE SHEET Directions: Solve the following problems. 1. The distance from the earth to the nearest star outside our solar system is approximately 25,700,000,000,000. When expressed in scientific notation, what is the value of n. 2.57 x 10n 2. One angstrom is 1 x 10-7 millimeter. When written in standard notation, how many zeros will your answer have? 3. One light year is approximately 5.87 x 1012 miles. Use scientific notation to express this distance in feet (Hint: 5,280 feet = 1 mile). 4. John travels regularly for his job. In the past five years he has traveled approximately 355,000 miles. Convert his total miles into scientific notation. 5. The mass of one proton is approximately 1.7 x 10-24 gram. Us89Q V ^ _ i l o       # & 1 4 ? 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