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Companion slides for Basic Laboratory Calculations for Biotechnology by Lisa A. Seidman, Ph.D.

Companion slides for Basic Laboratory Calculations for Biotechnology by Lisa A. Seidman, Ph.D. textbook: ISBN 978-0-13-223810-6. scientific calculator. MATH IS A TOOL! (IT DOESN’T MATTER WHETHER OR NOT YOU “LIKE” IT).

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Companion slides for Basic Laboratory Calculations for Biotechnology by Lisa A. Seidman, Ph.D.

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  1. Companion slides for Basic Laboratory Calculations for Biotechnology by Lisa A. Seidman, Ph.D.

  2. textbook: ISBN 978-0-13-223810-6 scientific calculator

  3. MATH IS A TOOL! (IT DOESN’T MATTER WHETHER OR NOT YOU “LIKE” IT)

  4. In Japan and Taiwan, people believe that hard work leads to good performance in math • In the United States, people believe one is either born with this ability or not • The ability to use math is not a genetic gift but rather is learned with practice!

  5. Problem Solving Tips: • Keep track of units and record them!!!!! • Keep track of all information. • Use simple sketches, flowcharts, arrows, or other visual aids to help define problems. • Check that each answer makes sense in the context of the problem. (Reasonableness Test) • State the answer clearly; remember the units. • Watch for being “off by a power of 10”.

  6. Chapter 1 Exponents and Scientific Notation

  7. Exponents An exponent is used to show that a number is to be multiplied by itself a certain number of times. 24 = 2 x 2 x 2 x 2= 16 exponent 24 base

  8. Box 1 Calculations Involving Exponents • To multiply two numbers with exponents where the numbers have the same base, add the exponents: • am X an = am n + examples: 53 x 56 = 59 23 x 22 = 25 = 32

  9. Box 1 Calculations Involving Exponents • 2. To divide two numbers with exponents where the numbers have the same base, subtract the exponents: • = am n am - an examples: 53/56 = 53-6 = 5-3 2-3/2-4 = 2(-3)-(-4) = 21 = 2

  10. Box 1 Calculations Involving Exponents • 3. To raise an exponential number to a higher power, multiply the two exponents. (am)n = am X n examples: (23)2 = 26 (103)-4 = 10-12

  11. Box 1 Calculations Involving Exponents • 4. To multiply or divide numbers with exponents that have different bases, convert the numbers with exponents to their corresponding values without exponents. Then, multiply or divide. example: multiply 32 X 24 = ? 32 = 9 and 24 = 16, so 9 X 16 = 144

  12. Box 1 Calculations Involving Exponents • 4 (continued). To multiply or divide numbers with exponents that have different bases, convert the numbers with exponents to their corresponding values without exponents. Then, multiply or divide. example: divide 4-3/ 23 = ? 4-3 = X X = = 0.015625 and 23 = 8 so = 0.001953125 1 1 1 1 4 64 4 4 0.015625 8

  13. Box 1 Calculations Involving Exponents • 5. To add or subtract numbers with exponents, convert the numbers with exponents to their corresponding values without exponents. example: 43 + 23 = 64 + 8 = 72

  14. Box 1 Calculations Involving Exponents • 6. By definition, any number raised to the 0 power is equal to 1. example: 850 = 1

  15. Convert a number to scientific notation Example #1 (number greater than 10): 5467 . . . . 3 1 2 Insert decimal Decimal was moved 3 spaces to the left, so exponent is 3: = 5.467 x 103

  16. Convert a number to scientific notation Example #2 (number less than 1) : 0.000348 1 . . . . 4 3 2 Decimal was moved 4 spaces to the right, so exponent is -4: = 3.48 x 10-4

  17. More about scientific notation 205. = 0.205 x 103 205. = 2.05 x 102 205. = 20.5 x 101 205. = 2050 x 10-1 205. = 20500 x 10-2 As coefficient gets larger, Exponent gets smaller!

  18. Calculations with Scientific Notation • To multiply numbers in scientific notation, use two steps:Step 1. Multiply the coefficients togetherStep 2. Add the exponents to which 10 is raised. • (2.34 x 102) (3.50 x 103) = • (2.34 x 3.5) x (102+3) = 8.19 x 105

  19. Calculations with Scientific Notation • 2. To divide numbers in scientific notation, use two steps: Step 1. Divide the coefficients Step 2. Subtract the exponents • (5.4 x 105)/ (2.4 x 103) = • (5.4/2.4) x (105-3) = 2.25 x 102

  20. Calculations with Scientific Notation 3.To add or subtract numbers in scientific notation If exponents are the same, just add or subtract the coefficients 3.0 x 104 2.5 x 104 5.5 x 104 +

  21. Calculations with Scientific Notation 3.To add or subtract numbers in scientific notation If exponents are notthe same, make them the same and add or subtract the coefficients (2.05 x 102) – (9.05 x 10-1) 2.05 x 102 -0.00905 x 102 2.04095 x 102

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