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