Examples of units with non-integer exponents

In summary, there are various situations where units with non-integer exponents can be seen. Examples include noise voltage density in electronics (\text{V}/\text{Hz}^\frac{1}{2}) and the statcoulomb (\text{cm}^\frac{3}{2}\cdot\text{g}^\frac{1}{2}/\text{s}), as well as in the rate equations for chemical kinetics and in the endurance parameter and cube loading calculations for airplanes. These types of units are considered "quite common", according to some sources.
  • #1
Chetlin
36
0
Hi everyone,

Would anyone be able to give me a few examples of places where units with non-integer exponents come up? I know of a couple right now: noise voltage density (?) in electronics has units [itex]\text{V}/\text{Hz}^\frac{1}{2}[/itex] and the statcoulomb has equivalent units [itex]\text{cm}^\frac{3}{2}\cdot\text{g}^\frac{1}{2}/\text{s}[/itex].

Are there many other places? One answer here on Stack Overflow says that they are "quite common" but I can't think of any other places where they come up.

Thanks!
 
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  • #2
When writing the rate equations in chemical kinetics problems we often see non integer exponents for the concentrations. This leads to some interesting units for other factors in the equations.
 
  • #3
The endurance parameter for an airplane is lift coefficient^3/2 divided by drag coefficient.
Cube loading is weight divided by wing area^3/2.
 

Related to Examples of units with non-integer exponents

1. What is a unit with a non-integer exponent?

A unit with a non-integer exponent is a measurement unit that is raised to a power that is not a whole number. This means that the unit is being multiplied or divided by itself a fractional number of times.

2. Can you provide an example of a unit with a non-integer exponent?

One example of a unit with a non-integer exponent is the square root of meters, represented as m1/2. This means that the unit is being multiplied by itself 1/2 times, which is equivalent to taking the square root.

3. How is a unit with a non-integer exponent different from a unit with an integer exponent?

A unit with a non-integer exponent represents a fractional power, while a unit with an integer exponent represents a whole number power. This means that a unit with a non-integer exponent is a more precise measurement than a unit with an integer exponent.

4. What are some other examples of units with non-integer exponents?

Some other examples include cubic inches (in3), square feet (ft2), and inverse seconds (s-1). These units represent measurements such as volume, area, and frequency, respectively.

5. How are units with non-integer exponents useful in science?

Units with non-integer exponents are useful in science because they allow for more precise measurements. They are also used to represent physical quantities that cannot be expressed in whole numbers, such as square roots and inverse values. Additionally, they are important in mathematical calculations and equations.

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