Spreadsheet Models for Managers
Getting Access to Spreadsheet Models for Managers
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Spreadsheet Models for Managers
This reading is especially relevant for Session 2Dimensional Analysis
Dimensional analysis is a technique for designing or validating calculations involving quantities that have dimensions, or units. This page describes a technique you can use to figure out how to compute with dimensioned quantities.
- Dimensioned quantities
- Arithmetic with dimensioned quantities
- The fundamental trick
- Examples
- Examples with metric units
Dimensioned quantities
A dimensioned quantity is a number with attached units. For example, your age is a dimensioned quantity — 29 years, say. Or 914544000 seconds. Expressed this way, the units of your age would be years or seconds, respectively.
Whenever we perform arithmetic with dimensioned quantities, the units must be consistent and make sense. You can use this fact to figure out what gets multiplied by what. But to do that, you must understand the rules of arithmetic with dimensioned quantities.
<snip>…
Some of the page you’ve been reading has been suppressed from this sampler. To see the complete version of this article, why not order the full course? It’s available at this Web site or in downloadable format.
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…<end snip>
Sounds easy enough. Viewed as dimensional quantities, we can express this as:
Total space = 1000 m2+ 800 m2 = 1800 m2
If we were to double our space instead, we would multiply our current space by the “pure number” 2:
Total space = 2 * 1000 m2 = 2000 m2
We want to carpet the combined space. Carpet tiles are squares with each side measuring 0.5 meters. How many carpet tiles will we need?.
Total square yards = Total space = 1800 m2 * (1 tile)/(0.5 m2)
= 7200 tiles
Here we used the fact that multiplying by 1, in the form
1 = (1 tile)/(0.5 m2),
doesn’t change the value of the dimensioned quantity.
Last Modified: Wednesday, 27-Apr-2016 04:15:26 EDT
For many of you, matrix multiplication and array arithmetic are new ideas. It’s easy to get lost in the details of how they work and then forget about why we use them.
To keep a clear view of the forest and avoid focusing only on the trees, remember why we use matrix multiplication and array arithmetic. Briefly, we use them because we find that it’s very often helpful to decompose a problem into parts (analysis), then do calculations on the parts, and finally reassemble the final solution from the results of those partial calculations (synthesis).
Matrix multiplication and array arithmetic provide us with very convenient methods for performing those intermediate calculations on the parts. They’re the tools that make analysis and synthesis so powerful.