Concept explainers
Carry out the following conversions: (a) 22.6 m to decimeters, (b) 25.4 mg to kilograms, (c) 556 mL to liters, (d)
Interpretation: The given conversions are to be carried out by dimensional analysis.
Concept introduction:
Dimensional analysis is a way to convert units of measurement. In order to convert from one unit to another, we need to know the relationship between those units. These relationships are called conversion factors. Dimensional analysis is used to set up and solve a unit conversion problem using conversion factors.
The conversion factor is a fraction obtained from a relationship between the units. It is written as a ratio and can be inverted to give two conversion factors for every relationship.
Answer to Problem 56QP
Solution:
a)
b)
c)
d)
Explanation of Solution
a)
Convert the quantity
The conversion factors for the relationship
Now, set up the unit conversion problem using the appropriate conversion factor.
The units in the conversion factor must cancel to give the correct unit for the answer.
Hence,
b)
Convert the quantity
The conversion factors for the relationship
The conversion factors for the relationship
Now, set up the unit conversion problem using the appropriate conversion factors.
The units in the conversion factor must cancel to give the correct unit for the answer.
Hence,
c)
Convert the quantity
The conversion factors for the relationship
Now, set up the unit conversion problem using the appropriate conversion factor.
The units in the conversion factor must cancel to give the correct unit for the answer.
Hence,
d)
Convert the quantity
The conversion factors for the relationship
The conversion factors for the relationship
Now, set up the unit conversion problem using the appropriate conversion factors.
The units in the conversion factor must cancel to give the correct unit for the answer.
Hence,
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Chapter 1 Solutions
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