Question: 43: The area of a rectangular field (in \mathrm{m}^{2} ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is
(1) 1382.5
(2) 14 \times 10^{2}
(3) 138 \times 10^{1}
(4) 1382
Answer: Option (2)
Explanation:
The area of a rectangular field is given by \text{Area} = \text{length} \times \text{breadth}.
Substituting the given values, \text{Area} = 55.3 \times 25.
Calculating, \text{Area} = 1382.5 \ \mathrm{m}^2.
Now, we apply the rule of significant figures. The length 55.3 m has 3 significant figures,
while the breadth 25 m has 2 significant figures.
In multiplication, the result should be reported with the least number of significant figures, which is 2.
Rounding 1382.5 to 2 significant figures gives 1.4 \times 10^{3},
which can also be written as 14 \times 10^{2}.
Hence, the correct answer is Option (2).