Units And Measurement

The given relation is . The formula for relative error (or percentage error if multiplied by 100) when quantities are multiplied or divided is: If , then . For percentage errors: Given percentage errors: (Note: C in formula is uppercase, observable is c. Assuming c=C) Percentage error in P = . We assume as it's usually a power. So, Divide by 0.5 (or multiply by 2): . Let's recheck the options. The checkmark is on (d) . If . Then . So, . This is FALSE. My calculation for yields . This is correct. So . This is option (a). The checkmark in the image is on option (d) . But my derivation gets . Let's re-read "The percentage errors in a, b, c and d are 0.5% in each". So . So . Since is usually a positive constant in such formulas or if not specified, assume . . This is option (a). The checkmark on (d) appears to be incorrect based on my derivation. If , then . This is not 2%. I will proceed with my derived answer . Option (a) is . The checkmark is on (d) . There is a discrepancy. I'll use my derived value and note that the marked option might be different.

The units given are all used to measure length but vary greatly in magnitude:
- A parsec is a very large unit used to measure astronomical distances, equal to approximately 3.26 light years.
- A nanometer is 10^{-9} meters, often used to measure atomic and molecular distances.
- A fermi (also known as a femtometer) is meters, the smallest unit listed here, used to measure nuclear sizes.
- An angstrom is meters, used to measure atomic dimensions, but larger than a fermi.
Among these, the fermi is the smallest unit for length. Therefore, the correct answer is option (3), fermi.

Among the given options, the measurement is expressed in scientific notation with the smallest exponent, making it the most accurate measurement.

We are given:
Given:

• are lengths dimension
• is density dimension

Hence, the physical quantity is mass.