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)

oIn Japan and Taiwan, people believe that hard work leads to good performance in math

oIn the United States, people believe one is either born with this ability or not

oThe ability to use math is not a genetic gift but rather is learned with practice!

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”.

Chapter 1

Exponents and Scientific Notation

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

24

base

exponent

Box 1Calculations Involving Exponents

1. 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

Box 1Calculations Involving Exponents

2. To divide two numbers with exponents where the numbers have the same base, subtract the exponents:

= am n-

examples: 53/56 = 53-6 = 5-3

2-3/2-4 = 2(-3)-(-4) = 21 = 2

am

an

Box 1Calculations Involving Exponents

3. To raise an exponential number to a higher power, multiply the two exponents.

examples: (23)2 = 26

(103)-4 = 10-12

(am)n = am X n

Box 1Calculations 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

Box 1Calculations 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

14

14

14

164

0.015625

8

Box 1Calculations 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

Box 1Calculations Involving Exponents

6. By definition, any number raised to the 0 power is equal to 1.

example: 850 = 1

Convert a number to scientific notation

Example #1 (number greater than 10):

5467.

Insert decimal23 1...

Decimal was moved 3 spaces to the left, so exponent is 3:

= 5.467 x 103

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

42 3

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 getslarger,

Exponent gets smaller!

Calculations with Scientific Notation

1. 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

Calculations with Scientific Notation

2. To divide numbers in scientific notation, use two steps:

Step 1. Divide the coefficientsStep 2. Subtract the exponents

(5.4 x 105)/ (2.4 x 103) =

(5.4/2.4) x (105-3) = 2.25 x 102

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

+

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 102) – (9.05 x 10-1)

2.05 x 102

-0.00905 x 102

2.04095 x 102