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Dimensional analysis is used to convert units.
The Principle Behind Dimensional Analysis
The guiding principle of dimensional analysis is that you can
multiply anything by �1� without changing the meaning. An equality
set into a fraction formation = 1. For example, if x = y, then x/y
= 1 and y/x = 1. Therefore, the equalities can be set into
fractions and multiplied to convert units.
Another concept necessary to understanding
dimensional analysis is that units that are on the top and bottom of
an expression cancel out.
Equalities Commonly used in Dimensional
Analysis
Several equalities are used often in chemistry.
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Equalities commonly used in chemistry
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| 4.18 J |
1.00 cal |
| 1 � |
10‑10 m |
| 1 cm3 |
1 mL |
| 1 dm3 |
1 L |
| 1 in |
2.54 cm |
| 1 kg |
2.2 lb |
| 1 atm |
101.3 kPa |
| 1 atm |
760 mm Hg |
| 1 mole |
6.02 � 1023 pieces |
Metric prefixes are also used to form equalities
between different metric units.
Dimensional Analysis
To work dimensional analysis problems:
- Write your known down on the left side
- Write down �=__________ [desired unit]� at the right
side
- Identify equalities that will get you from the known
information to the desired unit. If there is no equality
that involves both the known and unknown, you�ll have to
find more than one to more than one step.
- Arrange the equalities into a fractional form so that
the known unit will cancel out and the desired unit will be
left.
- Multiply across the top of the expression and divide
numbers on the bottom.
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