This document discusses scientific notation. It begins by defining scientific notation as a way for scientists to express extremely large or small numbers using exponents. It then provides examples of writing numbers in scientific notation by positioning the decimal point and determining the appropriate exponent. The document also demonstrates how to convert numbers written in scientific notation to a standard numerical form without exponents. Finally, it shows how to perform calculations using numbers expressed in scientific notation.

1. Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
2
Exponents and
Polynomials
12

2. Slide - 2Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
1. Express numbers in scientific notation.
2. Convert numbers in scientific notation to
numbers without exponents.
3. Use scientific notation in calculations.
Objectives
12.3 An Application of Exponents: Scientific
Notation

3. Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Express Numbers in Scientific Notation
Numbers occurring in science are often extremely large
or extremely small. Because of the difficulty of working
with many zeros, scientists often express such numbers
with exponents, using a form called scientific notation.
In scientific notation, there is always one nonzero digit
before the decimal point.

4. Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Express Numbers in Scientific Notation
Writing a Number in Scientific Notation
A number is written in scientific notation when it is
expressed in the form
where and n is an integer.
10 ,n
a
1 10a 

5. Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Writing a Number in Scientific Notation
Step 1 Position the decimal point. Place a caret ^ to the right
of the first nonzero digit, where the decimal point will
be placed.
Step 2 Determine the numeral for the exponent. Count the
number of digits from the decimal point to the caret.
This number gives the absolute value of the exponent
on 10.
Step 3 Determine the sign for the exponent. Decide whether
multiplying by 10n should make the result of Step 1
greater or less.
• The exponent should be positive to make the result greater.
• The exponent should be negative to make the result less.
Express Numbers in Scientific Notation

6. Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
(a) 153,000,000,000
Example
Write each number in scientific notation.
Express Numbers in Scientific Notation
Reading from left to right, the first nonzero digit is 1. So, we
will put the decimal point to the right of 1. Since the (invisible)
decimal point was to the right of the last zero, we will have to
move it to the left 11 places. And, since we moved it to the left,
the 11 will be positive. Thus,
153,000,000,000 = 1.53 1011

7. Slide - 7Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
(b) 9547.3
Example (cont)
Write each number in scientific notation.
Express Numbers in Scientific Notation
Reading from left to right, the first nonzero digit is 9. So, we
will put the decimal point to the right of 9. Since the decimal
point was to the right of 7, we will have to move it to the left 3
places. And, since we moved it to the left, the 3 will be positive.
Thus,
9547.3 = 9.5473 103

8. Slide - 8Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
(c) 0.00000005842
Example (cont)
Write each number in scientific notation.
Express Numbers in Scientific Notation
Reading from left to right, the first nonzero digit is 5. So, we
will put the decimal point to the right of 5. Since the decimal
point was to the right of the first 0, we will have to move it to
the right 8 places. And, since we moved it to the right, the 8
will be negative. Thus,
0.00000005842 = 5.842 10–8

9. Slide - 9Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
(d) 6.1134
Example (cont)
Write each number in scientific notation.
Express Numbers in Scientific Notation
Here, the decimal point is already to the right of the first
nonzero number, 6. Thus, we do not have to move it, and the
exponent of 10 will be 0.
6.1134 = 6.1134 100

10. Slide - 10Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
(a) 4.125 105
Example
Write each number without exponents.
Convert Numbers in Scientific Notation
Since the exponent of 10 is positive 5, we will move the decimal
to the right (undoing the scientific notation) 5 places, making
our final answer bigger than 4.
4.125 105 = 412,500
(b) 1.456 10–4
Since the exponent of 10 is negative 4, we will move the decimal
to the left 4 places, making our final answer smaller than 1.
1.456 10–4 = 0.0001456





11. Slide - 11Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
(a) (8 106)(3 10–4)
Example
Perform each calculation. Write answers in scientific notation and
also without exponents.
Use Scientific Notation in Calculations
= 2400
= (8 3)(106 10–4)
= (24)(102)
5
7
9 10
(b)
3 10


5
7
9 10
3 10
 
2
3 10
 
0.03