Question

perform the following operations expressing the answer in the correct number of significant figures.

1. 1.35 m × 2.467 m =
2. 1,035 m² ÷ 42 m =
3. 12.01 ml + 35.2 ml + 6 ml =
4. 55.46 g - 28.9 g =
5. 0.021 cm × 3.2 cm × 100.1 cm =
6. 0.15 cm + 1.15 cm + 2.051 cm =
7. 150 l³ ÷ 4 l =
8. 505 kg - 450.25 kg =
9. 1.252 mm × 0.115 mm × 0.012 mm =
10. 1.278 × 10³ m² ÷ 1.4267 × 10² m =

Explanation:

Step1: Multiply the values

$1.35\times2.467 = 3.33045$. For multiplication, the answer should have the same number of significant figures as the number with the fewest significant figures among the values being multiplied. 1.35 has 3 significant - figures and 2.467 has 4 significant - figures. So, the answer is rounded to 3 significant figures: $3.33\ m^{2}$.

Step2: Division of area by length is not a valid operation in terms of physical dimensions. This is an incorrect operation as $m^{2}\div m$ is not a standard physical operation in this context.

Step3: Add the values

$12.01 + 35.2+6=53.21$. For addition, the answer should be rounded to the same number of decimal places as the number with the fewest decimal places. 6 has 0 decimal places, so the answer is rounded to 53 mL.

Step4: Subtract the values

$55.46 - 28.9 = 26.56$. For subtraction, the answer should be rounded to the same number of decimal places as the number with the fewest decimal places. 28.9 has 1 decimal place, so the answer is 26.6 g.

Step5: Multiply the values

$0.021\times3.2\times100.1 = 6.72672$. 0.021 has 2 significant figures, 3.2 has 2 significant figures, and 100.1 has 4 significant figures. The answer is rounded to 2 significant figures: $6.7\ cm^{3}$.

Step6: Add the values

$0.15 + 1.15+2.051 = 3.351$. 0.15 and 1.15 have 2 decimal places, so the answer is rounded to 3.35 cm.

Step7: Divide the values

$150\div4 = 37.5$. 4 has 1 significant figure, so the answer is rounded to 1 significant figure: $40\ L^{2}$.

Step8: Subtract the values

$505 - 450.25 = 54.75$. 505 has 3 significant figures and 450.25 has 5 significant figures. The answer is rounded to 3 significant figures: $54.8\ kg$.

Step9: Multiply the values

$1.252\times0.115\times0.012 = 0.00172092$. 0.012 has 2 significant figures, so the answer is rounded to 2 significant figures: $1.7\times10^{-3}\ mm^{3}$.

Step10: Division of area by length is not a valid operation in terms of physical dimensions. This is an incorrect operation as $m^{2}\div m$ is not a standard physical operation in this context.

Answer:

1. $3.33\ m^{2}$
2. Invalid operation
3. $53\ mL$
4. $26.6\ g$
5. $6.7\ cm^{3}$
6. $3.35\ cm$
7. $40\ L^{2}$
8. $54.8\ kg$
9. $1.7\times10^{-3}\ mm^{3}$
10. Invalid operation