Download Use Scientific Notation Scientific Notation is a way to represent very

Use Scientific Notation
Scientific Notation is a way to represent very large and very small numbers. It is
usually in the form c 10 n where 1  c  10 and n is an integer.
Examples of Numbers in Scientific Notation
Number 
Two Million
Five Thousandths

Standard Form
2,000,000
0.005
Scientific Notation
2 10 6
5 103
Examples Writing Numbers in Scientific Notation

Write 42,590,000 ins scientific notation.
Move the decimal 7 places to the left, the exponent is 7.
42,590,000  4.259 107
Write 0.0000574 in scientific notation.
Move the decimal 5 places to the left, the exponent is -5.
0.0000574  5.74 105

Examples Writing Numbers in Standard Form
Write2.0075 10 6 in standard form.
Move the decimal 6 places to the right.
2.0075 106  2,007,500
4
 Write 1.685 10 in standard form
Move the decimal 4 places to the left.
1.685 104  0.0001685

 Ordering Numbers in Scientific Notation
Example
8
Order 103,400,
 7.8 10 , and 80,760,000 from least to greatest.
Solution:
1. Write each number in scientific notation.
103,400,000  1.034 10 8



80,760,000  8.076 10 7
2. Order the numbers. First order by powers of 10, then order the numbers
with the same power of 10.
8.076 107,1.034 108,7.8 108
Examples Computing with Numbers in Scientific Notation
8.5 10 1.7 10 
2
6
8.5 10 1.7 10  8.5 1.710
2
6
2
10 6 
14.45 10 8

1.445 10 10
1
8
1.445 10 9
1.5 10 
3 2




1.5 10   1.5
3 2
2
106  2.25 106
1.2 10 4
1.6 103
1.2 10 4 1.2 10 4

 3  0.75 10 7
3
1.6 10
1.6 10
1
7.5 10 107
7.5 10 6
Try These:
5
4
 Order the following numbers 2.7 10 , 3.40110 , and 27,500 from least to greatest.

Evaluate the expression:

1.3 10 
4.5 10 5
1.5 102
5 2


1.110 4.2 10 
7

2