Dimensional Analysis: Subtracting Units & Unitless Numbers

In summary, the conversation discusses dimensional analysis and the question of whether a dimensionless number can be subtracted from a quantity with a unit. It is clarified that only like units can be added or subtracted and dimensionless numbers cannot be added or subtracted to quantities with units. The conversation also mentions an example of 2[in]-1 where the 1 is dimensionless and the 2 has units of [in], and the conclusion is that this cannot be subtracted.
  • #1
nosequeponer
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this question is about dimensional analysis involving a number with units and a number with no units, if the question is already answered in another post please redirect me if not here is a simple example, for example, :

say i have 2[in]-1. the 1 is dimensionless and the 2 has units of [in]. can I subtract the
2[in]-1=1[in]?or do i leave it as 2[in]-1.

this is not from a problem. i was doing dim. analysis on a sol. and ended up with this so i knew i did something wrong, but it got me wondering what to do in a problem that might be stated like this say in a multiple choice.

thanks for the time.
 
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  • #2
nosequeponer said:
this question is about dimensional analysis involving a number with units and a number with no units, if the question is already answered in another post please redirect me if not here is a simple example, for example, :

say i have 2[in]-1. the 1 is dimensionless and the 2 has units of [in]. can I subtract the
2[in]-1=1[in]?or do i leave it as 2[in]-1.

Uh, no, you can't just promote pure numbers to dimensions having units on a whim. I'm not sure what 2 in. - 1 (pure number) even means.
this is not from a problem. i was doing dim. analysis on a sol. and ended up with this so i knew i did something wrong, but it got me wondering what to do in a problem that might be stated like this say in a multiple choice.

thanks for the time.

You can add and subtract only like units. Dimensionless numbers have no units, thus they cannot be added or subtracted to any quantities which contain units.
 
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Likes nosequeponer
  • #3
SteamKing said:
Uh, no, you can't just promote pure numbers to dimensions having units on a whim. I'm not sure what 2 in. - 1 (pure number) even means.You can add and subtract only like units. Dimensionless numbers have no units, thus they cannot be added or subtracted to any quantities which contain units.
ok thanks for taking the time and clarifying.
 

Related to Dimensional Analysis: Subtracting Units & Unitless Numbers

1. What is dimensional analysis?

Dimensional analysis is a mathematical method used to convert between different units of measurement. It involves multiplying or dividing by conversion factors to ensure that the units cancel out and the final result is in the desired units.

2. Why is dimensional analysis important in science?

Dimensional analysis is important in science because it allows scientists to accurately measure and compare physical quantities without having to memorize conversion formulas for each unit. It also helps to prevent errors in calculations and ensures that the units of the final result are correct.

3. How do you subtract units using dimensional analysis?

To subtract units using dimensional analysis, you should first convert all units to the same base unit using conversion factors. Then, simply subtract the numerical values and keep the units of the base unit. For example, to subtract 10 meters from 2 kilometers, first convert 10 meters to 0.01 kilometers. Then subtract 2 - 0.01 = 1.99 kilometers.

4. Can you subtract a unitless number from a unit?

Yes, you can subtract a unitless number from a unit. This is because unitless numbers do not have any units attached to them, so they do not affect the units of the final result. However, it is important to make sure that all units are converted to the same base unit before subtracting.

5. What are some common mistakes to avoid when using dimensional analysis?

Some common mistakes to avoid when using dimensional analysis include not converting all units to the same base unit, forgetting to include conversion factors, and using incorrect conversion factors. It is also important to pay attention to the units of the final result and make sure they make sense in the context of the problem.

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