Question

The area of rectangular field (in m²) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is:

• A. 138 x 101
• B. 1382
• C. 1382.5
• D. 14 x 10²

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When multiplying or dividing physical quantities, the number of significant digits in the final result must not exceed the number of significant digits in the least precise value used in the calculation.
Step 2: Detailed Explanation:
1. Identify significant digits:
Length (\(L\)) = 55.3 m \(\rightarrow\) 3 significant digits.
Breadth (\(B\)) = 25 m \(\rightarrow\) 2 significant digits.
The least number of significant digits is 2. Therefore, the answer must be rounded to 2 significant digits.
2. Perform the multiplication:
\[ \text{Area} = L \times B = 55.3 \times 25 = 1382.5 \text{ m}^2 \]
3. Rounding to 2 significant digits:
Rounding 1382.5 to two significant figures means focusing on the first two digits (1 and 3).
The next digit is 8, which is \(\ge 5\), so the 3 is rounded up to 4.
The value becomes 1400.
4. Scientific Notation:
1400 can be written as \(14 \times 10^2\). This clearly shows 2 significant digits.
Step 3: Final Answer:
The correctly rounded area is \(14 \times 10^2 \text{ m}^2\).