(Also called the factor-label method)
Dimensional analysis is a super useful technique used for many different reasons:
scaling up recipes to much larger quantities
Converting English-to-metric units (or vice-versa)
Physics problems, e.g. involving speed and distance
Chemistry problems (how much product is made from how much starting materials?)
Dimensional analysis is just a a trick in which we use conversions factors to get from the info we have, to the answer we need.
Sometimes we need to string several conversion factors together to get the answer that we need.
What is a conversion factor?
Two things that are exactly equivalent
We can always write 2 equivalent things as a fraction
The fraction can be written with either term on top, or bottom:
Conversion factor for money
Conversion factor for distance
Example: How do we convert inches to cm?
Convert days to seconds
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Science and Engineering Practices: 5. Using Mathematics and Computational Thinking:
Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m 3, acre-feet, etc.).
NSTA: The efficiency and effectiveness of the metric system has long been evident to scientists, engineers, and educators. Because the metric system is used in all industrial nations except the United States, it is the position of the National Science Teachers Association that the International System of Units (SI) and its language be incorporated as an integral part of the education of children at all levels of their schooling.