Units Dimensions And Measurements

Step 1: Formula for Density


Step 2: Calculating Density

Rounding to three significant figures:
Step 3: Conclusion

Since 2.19 g/cm³ is the correctly rounded value, Option (3) is correct.

Step 1: Understanding Error Propagation:
For any physical quantity defined by the relation , the maximum relative error is calculated by summing the products of the exponents and the relative errors of the individual quantities. The general formula is: (Note: Even if an exponent is negative in the formula, we take absolute values because we calculate the \maximum possible error).
Step 2: Substituting Given Values:
The question gives the percentage errors for X, Y, and Z. Percentage error is defined as . Given:

• Error in
• Error in
• Error in

Step 3: Calculation:
We want the percentage error in P, which is . Multiply the error propagation equation by 100: Substitute the given percentage values ( ) into the equation:
Step 4: Final Answer:
The percentage error in P is .

• Let relative error in area = ΔA/A = 0.08 = 8%.
• Area ∝ L\textsuperscript{2} so ΔA/A = 2(ΔL/L) → ΔL/L = 0.08/2 = 0.04.
• Volume ∝ L\textsuperscript{3} so relative error in volume ΔV/V = 3(ΔL/L) = 3 × 0.04 = 0.12 → 12%.
• Hence the percentage error in volume is 12% → option (2).

Terminal zeros in a number without a decimal point are ambiguous and may or may not be significant. Using scientific notation avoids confusion. All zeros between non-zero digits are always significant. Terminal zeros after a decimal point are significant.