Chemistry Reference
In-Depth Information
inch
3
be packed into a volume of 1 is 100 million cubed—about 1 million billion
billion! Each iron atom is almost unimaginably small.
EXAMPLE 2.8
To get an idea of how large a number 1 billion is, calculate the number of years
it would take to spend $1 billion if a person spent $1000 per day. (Assume that
there is no interest or other addition to the $1 billion.)
Solution
Days
year
Dollars
Daily rate
Days
Years
(
)
(
)
1 day
1000 dollars
1 year
365 days
1,000,000,000 dollars
= 2740 years
It would take over 2700 years to spend $1 billion by spending $1000 a day!
Just think how large the number 100 billion or 1 million billion billion is. Some
numbers common in science are even larger than these.
Practice Problem 2.8
Calculate the amount of money that you would
have to spend
per second
to use up $10 billion in 100 years.
Scientists handle large and small numbers using
exponential notation.
A
number written in this format has the following parts:
10
3
1.73
Coefficient
Base
Exponent
Exponential part
The
coefficient
is an ordinary number that may or may not include a decimal point.
It is multiplied by an
exponential part,
consisting of a
base
and an
exponent.
For
numbers used in scientific work, the base is usually 10, and the exponent is usu-
ally an integer (a whole number). The coefficient is multiplied by the base the num-
ber of times given by the exponent. That is, the number in the example is 1.73
multiplied three times by 10:
10
3
1.73
1.73
10
10
10
1730
Table 2.1 lists important exponential parts and their meanings. Thus we can
write 1 million in exponential notation as follows:
10
6
1,000,000
1
10
10
10
10
10
10
1
