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NEET PHYSICSMedium

The area of a rectangular field (in m2\text{m}^2) of length 55.355.3 m and breadth 2525 m after rounding off the value, for correct significant digits is:

A

14×10214 \times 10^2

B

138×101138 \times 10^1

C

1382

D

1382.5

Step-by-Step Solution

Area of the rectangle = Length ×\times Breadth Area = 55.3 m×25 m=1382.5 m255.3 \text{ m} \times 25 \text{ m} = 1382.5 \text{ m}^2. According to the rules for arithmetic operations with significant figures, in multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures . Here, the length (55.355.3 m) has 3 significant figures and the breadth (2525 m) has 2 significant figures. Therefore, the final result must be rounded off to 2 significant figures. 1382.5 m21382.5 \text{ m}^2 rounded off to 2 significant figures is 1400 m21400 \text{ m}^2, which is properly expressed in scientific notation as 1.4×103 m21.4 \times 10^3 \text{ m}^2 or 14×102 m214 \times 10^2 \text{ m}^2.

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