vdoc

52 Part I: Technical Mathematics
Negative Exponents
We can also use exponents to represent multiplication statements such as
Part I.F
1
2
× 1 1
2
× 2
=
The statement above is written as 2 –3 . In this case we use a negative exponent to
show that the number 2 is in the denominator. Note that 2 –3 can also be written as
1
8
1
2 3
meaning that 2 –3 and 2 3 are reciprocals. We read 2 –3 as “2 to the negative three
power.”
Powers of 10
Table 6.1 shows the powers of 10 and the numbers they represent. These powers of
10 are used in scientific notation.
SCIENTIFIC NOTATION
For very large or small values, it is often more convenient to represent a number in
terms of scientific notation. Scientific notation uses powers of 10. For example, the
number 100 can be written as 1 × 10 2 . The decimal 0.01 can be shown as 1 × 10 –2 .
Table 6.1 Powers of 10.
Exponent form Number
10 –6 0.000001
10 –5 0.00001
10 –4 0.0001
10 –3 0.001
10 –2 0.01
10 –1 0.1
10 0 1
10 1 10
10 2 100
10 3 1,000
10 4 10,000
10 5 100,000
10 6 1,000,000