How to Know if a Ratio Is Dimensionless

Step-by-Step Guide

1. 1

   Step 1: Express a ratio of two physical quantities as a fraction.

   This is the simplest way to determine whether it is dimensionless or not.
   
   To see how to make a ratio and express it as a fraction see Make a Ratio. , This reduces the possibility of making a mistake when trying to determine whether a ratio is dimensionless or not. , If they are, they will cancel each other out. , Sometimes, the units might appear as different, but in fact, one of them is derived and can be expressed as the other.
   
   For example, if the physical quantity above the fraction bar is force (unit is N) and below is a product of mass (kg) and a quotient of the distance traveled (m) and squared value of the time interval (s^2), the whole fraction would equal only a number (a dimensionless result), since =. , Some SI units have other forms, and they can be easily converted one into the other if their ratio is given.
   
   For example, mass can also be expressed in grams which is a kilogram divided by a thousand, or in ounces (0.028kg).
2. 2

   Step 2: Write the appropriate unit for each of the physical quantities.

3. 3

   Step 3: Check whether the unit above the fraction bar is the same as the one below.

4. 4

   Step 4: Check if some units are derived.

5. 5

   Step 5: Check if the physical quantities are expressed in SI units.

Detailed Guide

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