JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2025
- Easy
- MCQ
For an experimental expression \(y=\frac{32.3 \times 1125}{27.4}\), where all the digits are significant. Then to report the value of \(y\) we should write
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(y=1330\)
Step-by-step Solution
Detailed explanation
Explanation:
The provided answer key is completely correct. The preference for Option D usually happens when the rule for addition/subtraction is mistakenly applied instead of the rule for multiplication/division:
1. Rule for Multiplication and Division:
In operations involving multiplication and division, the final result must be rounded off to contain the same number of significant figures as present in the component term with the least number of significant figures.
2. Counting Significant Figures in the Given Terms:
- \( 32.3 \) has 3 significant figures.
- \( 1125 \) has 4 significant figures.
- \( 27.4 \) has 3 significant figures.
Since the minimum number of significant figures among the given values is 3, the final answer must be rounded off to exactly 3 significant figures.
3. Calculation and Rounding:
\( y = \frac{32.3 \times 1125}{27.4} = 1326.186... \)
Rounding off \( 1326.186... \) to 3 significant figures:
The first three digits are 1, 3, and 2. The fourth digit is 6 (which is greater than 5), so the third digit increases by 1, yielding \( 1330 \). In the number \( 1330 \), the trailing zero without a decimal point is not significant, leaving exactly 3 significant figures.
Option D (\( 1326.2 \)) has 5 significant figures, which violates the rounding rule for multiplication and division.
Hence, Option B is the correct choice.
The provided answer key is completely correct. The preference for Option D usually happens when the rule for addition/subtraction is mistakenly applied instead of the rule for multiplication/division:
1. Rule for Multiplication and Division:
In operations involving multiplication and division, the final result must be rounded off to contain the same number of significant figures as present in the component term with the least number of significant figures.
2. Counting Significant Figures in the Given Terms:
- \( 32.3 \) has 3 significant figures.
- \( 1125 \) has 4 significant figures.
- \( 27.4 \) has 3 significant figures.
Since the minimum number of significant figures among the given values is 3, the final answer must be rounded off to exactly 3 significant figures.
3. Calculation and Rounding:
\( y = \frac{32.3 \times 1125}{27.4} = 1326.186... \)
Rounding off \( 1326.186... \) to 3 significant figures:
The first three digits are 1, 3, and 2. The fourth digit is 6 (which is greater than 5), so the third digit increases by 1, yielding \( 1330 \). In the number \( 1330 \), the trailing zero without a decimal point is not significant, leaving exactly 3 significant figures.
Option D (\( 1326.2 \)) has 5 significant figures, which violates the rounding rule for multiplication and division.
Hence, Option B is the correct choice.
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