Dimensions, Unit Operations Homework (True/False)

• FAJISTE
In summary, X and Y are dimensionally different and cannot be added or subtracted. X and Y can be multiplied or divided, and X can be raised to a power or have a root taken. However, raising a constant to the power of a quantity is not physically meaningful. Therefore, the correct operations are X/Y, X*Y, X^2, Y^2, X^(1/3), and Y^(1/3).
FAJISTE

Homework Statement

X and Y are dimensionally different. (They have different units.) Select ALL the physically meaningful operations. State which are true or false
1. X/Y or X*Y
2. X+Y or X-Y
3. e^(X/Y) or e^(X+Y)
4. X^2 +Y^2 or X^X + Y^Y
5. X^2 or Y^2
6. X^(1/3) or Y^(1/3)

The Attempt at a Solution

I'm assuming

1. True because you could have like velocity/second, etc.
2. False, you can't add apples and oranges
3. False no idea though
4. False
5. True
6. True

An explanation along with the correct answers would be greatly appreciated.

FAJISTE said:
1. True because you could have like velocity/second, etc.
2. False, you can't add apples and oranges
3. False no idea though
4. False
5. True
6. True

I believe you have all correct so far.

For 3, I don't think it is possible to raise a constant to the power of a quanity.
Else it'd be like saying 2^(4 kilograms) or e^(2 Newtons), it is physically meaningless.

thanks a lot, if I could just have a complete confirmation since I only have one last try to get it right in the computer

N/m i was right, thanks for the confirm tho

1. What are dimensions in science?

Dimensions in science refer to the physical quantities that describe an object or phenomenon, such as length, mass, time, temperature, and electric charge. These dimensions are often represented by symbols, such as L for length and T for time, and are used to express measurements in a consistent and standardized way.

2. What are unit operations in science?

Unit operations in science are standardized procedures or processes that are used to transform raw materials or chemicals into desired end products. These operations involve physical, chemical, or biological changes and are often used in the production of pharmaceuticals, food, and other consumer products.

3. Are dimensions and unit operations the same thing?

No, dimensions and unit operations are not the same thing. Dimensions refer to physical quantities, while unit operations refer to standardized procedures used in the production of products. However, dimensions play a crucial role in unit operations as they are used to express measurements and ensure consistency in the process.

4. True or False: Dimensions and unit operations are only used in chemistry and physics.

False. While dimensions and unit operations are commonly used in chemistry and physics, they are also used in other scientific fields such as engineering, biology, and environmental science. Any field that involves measurements and processes can utilize dimensions and unit operations.

5. How are dimensions and unit operations important in scientific research?

Dimensions and unit operations are important in scientific research as they provide a standardized and consistent way to measure and describe physical quantities and processes. This allows for accurate and replicable results, which are crucial in scientific experiments and studies. Dimensions and unit operations also allow for effective communication and collaboration between scientists in different fields.

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