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

5. Problem Solving Tips: 1.Keep track of units and record them!!!!! 2. Keep track of all information. 3.Use simple sketches, flowcharts, arrows, or other visual aids to help define problems. 4.Check that each answer makes sense in the context of the problem. (Reasonableness Test) 5.State the answer clearly; remember the units. 6.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. 2 4 = 2 x 2 x 2 x 2= 16 2424 base exponent

8. Box 1 Calculations Involving Exponents 1.To multiply two numbers with exponents where the numbers have the same base, add the exponents: a m X a n = a m n + examples: 5 3 x 5 6 = 5 9 2 3 x 2 2 = 2 5 = 32

9. Box 1 Calculations Involving Exponents 2. To divide two numbers with exponents where the numbers have the same base, subtract the exponents: = a m n - examples: 5 3 /5 6 = 5 3-6 = 5 -3 2 -3 /2 -4 = 2 (-3)-(-4) = 2 1 = 2 amam anan

10. Box 1 Calculations Involving Exponents 3. To raise an exponential number to a higher power, multiply the two exponents. examples: (2 3 ) 2 = 2 6 (10 3 ) -4 = 10 -12 (a m ) n = a m X n

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 3 2 X 2 4 = ? 3 2 = 9 and 2 4 = 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 / 2 3 = ? 4 -3 = X X = = 0.015625 and 2 3 = 8 so = 0.001953125 1 4 1 4 1 4 1 64 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: 4 3 + 2 3 = 64 + 8 = 72

14. Box 1 Calculations Involving Exponents 6. By definition, any number raised to the 0 power is equal to 1. example: 85 0 = 1

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

16. Convert a number to scientific notation Example #2 (number less than 1) : 0.000348. 1... Decimal was moved 4 spaces to the right, so exponent is -4: = 3.48 x 10 -4 423

17. More about scientific notation 205. = 0.205 x 10 3 205. = 2.05 x 10 2 205. = 20.5 x 10 1 205. = 2050 x 10 -1 205. = 20500 x 10 -2 As coefficient gets larger, Exponent gets smaller!

18. Calculations with Scientific Notation 1.To multiply numbers in scientific notation, use two steps: Step 1. Multiply the coefficients together Step 2. Add the exponents to which 10 is raised. (2.34 x 10 2 ) (3.50 x 10 3 ) = (2.34 x 3.5) x (10 2+3 ) = 8.19 x 10 5

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 10 5 )/ (2.4 x 10 3 ) = (5.4/2.4) x (10 5-3 ) = 2.25 x 10 2

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 10 4 2.5 x 10 4 5.5 x 10 4 +

21. Calculations with Scientific Notation 3.To add or subtract numbers in scientific notation If exponents are not the same, make them the same and add or subtract the coefficients (2.05 x 10 2 ) – (9.05 x 10 -1 ) 2.05 x 10 2 -0.00905 x 10 2 2.04095 x 10 2