Chemistry Reference
In-Depth Information
Table 2.1
Important Exponential Parts and Their Meanings
Exponential Part
Value
Meaning
10
9
0.000000001
One-billionth
10
6
0.000001
One-millionth
10
3
0.001
One-thousandth
10
2
0.01
One-hundredth
10
1
0.1
One-tenth
10
0
1
One
10
1
10
Ten
10
2
100
One hundred
10
3
1000
One thousand
10
6
1,000,000
One million
10
9
1,000,000,000
One billion
Scientists generally report numbers in exponential notation with coefficients
that have one and only one integer digit, and that digit is not zero. That is, the
coefficient is a number that is greater than or equal to 1 and less than 10. Num-
bers in this format are said to be written in
standard exponential form,
or
sci-
entific notation.
Ascientific calculator gives exponential numbers in this form,
unless “engineering format” is selected. See Appendix 1 for methods of han-
dling numbers in exponential format with a scientific calculator.
In standard exponential nota-
tion, the coefficient is 1 or more
but less than 10.
EXAMPLE 2.9
Which one(s) of the following numbers is (are) written in scientific notation?
(a)
10
8
10
3
10
4
10
0
0.131
(b)
73
(c)
2.01
(d)
1.66
10
2.5
(e)
1.001
Solution
10
8
(a)
The number is not in scientific notation because the integer
digit of its coefficient is zero.
0.131
10
3
(b)
The number
73
is not in scientific notation because its coefficient
is a two-digit integer.
10
4
(c)
The number is in scientific notation because the coefficient
has only one integer digit and the exponent is an integer.
2.01
10
0
(d)
The number
1.66
is in scientific notation. The zero exponent is
permitted.
10
2.5
(e)
The number
1.001
is not in scientific notation because the
exponent is not an integer.
Practice Problem 2.9
Which of the following numbers is in scientific
notation?
(a)
10
2
10
2.1
10
3
4.000
(b)
0.500
(c)
6.51
