Significant Figures Questions in English

(D) To find the sum of physical quantities,we add the given values: $52.01 \ m + 153.2 \ m + 0.123 \ m = 205.333 \ m$.
According to the rules of significant figures for addition,the final result should be reported to the same number of decimal places as the measurement with the fewest decimal places.
The values are $52.01$ (two decimal places),$153.2$ (one decimal place),and $0.123$ (three decimal places).
The measurement with the fewest decimal places is $153.2 \ m$,which has one decimal place.
Therefore,we round the sum $205.333 \ m$ to one decimal place,which gives $205.3 \ m$.

(B) Density $\rho = \frac{\text{Mass}}{\text{Volume}}$.
Mass $m = 5.580 \text{ kg}$.
Side length $a = 9.0 \text{ cm} = 9.0 \times 10^{-2} \text{ m}$.
Volume $V = a^3 = (9.0 \times 10^{-2} \text{ m})^3 = 729 \times 10^{-6} \text{ m}^3 = 7.29 \times 10^{-4} \text{ m}^3$.
Density $\rho = \frac{5.580 \text{ kg}}{7.29 \times 10^{-4} \text{ m}^3} \approx 7654.32 \text{ kg m}^{-3} = 7.65432 \times 10^3 \text{ kg m}^{-3}$.
Since the side length $9.0 \text{ cm}$ has only two significant figures,the final result must be rounded to two significant figures.
Rounding $7.65432$ to two significant figures gives $7.7$.
Therefore,$X = 7.7$.