The area of rectangular field (in ${\text{m}}^2$) of length $55.3\text{m}$ and breadth $25\text{m}$ after rounding off the value for correct significant digits is:

Area $=\text{length}\times \text{breadth}=55.3\times 25=1382.5{\text{m}}^2$.In multiplication, the result must be rounded to the same number of significant figures as the term with the fewest significant figures.$55.3$ has $3$ significant figures.$25$ has $2$ significant figures.Thus, the result must be rounded to $2$ significant figures.$1382.5$ rounded to $2$ significant figures is $1400$, which is written in scientific notation as $14\times 10^2$ or $1.4\times 10^3$.