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# 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

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.

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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.