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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
4
2
base
exponent
Box 1
Calculations 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:
5 3 x 5 6 = 59
23 x 22 = 25 = 32
Box 1
Calculations Involving Exponents
2. To divide two numbers with exponents
where the numbers have the same base,
subtract the exponents:
am
m- n
n
=
a
a
examples:
53/56 = 53-6 = 5-3
2-3/2-4 = 2(-3)-(-4) = 21 = 2
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
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
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 = 1 X 1 X 1 = 1 = 0.015625
4
4
4
64
and 23 = 8
so
0.015625
8
= 0.001953125
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
Box 1
Calculations 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
.. ..
3 2
1
Insert decimal
Decimal was moved 3 spaces to the left, so
exponent is 3:
= 5.467 x
3
10
Convert a number to scientific notation
Example #2 (number less than 1) :
0.000348
... .
1
2 3 4
Decimal was moved 4 spaces to the right,
so exponent is -4:
= 3.48 x
-4
10
More about scientific notation
205.
205.
205.
205.
205.
=
=
=
=
=
0.205 x 103
2.05 x 102
20.5 x 101
2050 x 10-1
20500 x 10-2
As coefficient gets
larger,
Exponent gets smaller!
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 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 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
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