| 
>>
View the other Key Equations and Concepts in this
chapter
Unit Conversion
Most unit conversions are done using a technique called dimensional
analysis, the factor-unit method, or the factor-label method. This
method consists of canceling units by multiplying by 1. This works
because multiplying by 1 does not change a value. It also works
because a value over the same value is equal to 1. Some of these
equivalences are the same as those indicated by the SI prefix relationships.
>> Example 1
How many centimeters are in 7.51 m?
Solution:
7.51 m |
|
= 751 cm |
There are three significant figures. Since metric prefixes are
defined, the relationship has infinite significant figures.
It doesn't matter how many times the value is multiplied
by 1, so you don't need a relationship for every conversion
but can use a series of relationships to a central unit.
>> Example 2
How many centimeters are in 208.0  m?
Solution:
There are 100 cm = 1 m and 1,000,000 m = 1 m, so
| 208.0 m |
| 1 m |
|
| 1,000,000 m |
|
|
|
= 0.02080 cm |
Hint: When doing a long series of conversions on your
scientific calculator, ignore all values of 1 (it's just a chance
to hit the wrong button), use the "" button before each
number that appears on the top of a conversion and the " " button before each number on the bottom. With this method it is
unnecessary to use your parenthesis buttons. You would enter the
preceding problem as "208.0 1,000,000100 =."
Most of the time, the starting unit is on the top. Occasionally,
this is not the case. When the unit is on the bottom of a fraction,
it will be represented as "u–1" or "/ u",
or use the term per before the unit.
>> Example 3
What is 9.5 min–1 in Hz?
Solution:
Recall that Hz is the same as s–1.
|
|
|
|
= 0.16 min–1 |
It is also possible to need to change units on both the top and
the bottom. In this case, treat each unit separately. It doesn't
matter whether you do the top or the bottom unit first.
>> Example 4
What is the speed in km/s of a car going 65.0 mph?
Solution:
Miles per hour is abbreviated as mph or mi/hr. The needed conversions
are 1.6 km = 1 mi, 60 s = 1 min, and 60 min = 1 hr.
There are only two significant figures. The "weak link" was the
conversion to km from miles. Although SI-to-SI conversions are
exact, when the unit system changes, the values are measured or
approximate. The interpretation of "1.6 km = 1 mi" is that a measured
1.6 km is exactly 1 mile. The time conversions are exact.
You could enter this conversion in your calculator as
65.01.6
60 60 =
Sometimes unit conversions are given as part of the problem.
>> Example 5
How many cents will it cost to buy 48.0 oz of meat at $1.89/lb?
Solution:
The problem tells you that 1 lb = $1.89. You also need to know
that 16 oz = 1 lb (exactly, the unit system is the same) and that
100 cents = $1.
In this problem the answer has three significant figures because
of the price per pound and the starting value. It is also fair
to use common sense and realize that this is a situation that
would not recognize a fraction of a cent.
Derived units, such as cm2 or m3, can also
have derived conversions. For example, since1 m = 100 cm, (1 m =
100 cm)2, and 1 m2 = 10,000 cm2.
>> Example 6
What is the volume in m3 of a 0.711-in3 box?
Solution:
Since 1 in = 2.54 cm, (1) 3 in3 = (2.54)
3 cm2,1 in3 = 16.387 cm3
and 100 cm = 1 m, (100)3 cm3 = (1)3
m3,so 1,000,000 cm3 = 1 m3.
| 0.711 in3 |
|
|
|
|
= 1.17 x 10–5 m3 |
>> View
the other Key Equations and Concepts in this chapter
|
