NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Mathematics in Physics
NEET · Physics · Mathematics in Physics
Read the following statements carefully: Statement I: The integer...
Read the following statements carefully:
Statement I: The integer used to divide the sum of measurements when calculating an average is an exact number with infinite significant figures.
Statement II: If a raw calculated mean is , it is rounded to to retain 3 significant figures.
Statement III: The sum of and has three significant figures.
Statement IV: When averaging measurements of the same precision, the final result retains the same number of decimal places as the original measurements.
How many of the above statements are correct?
Statement I: The integer used to divide the sum of measurements when calculating an average is an exact number with infinite significant figures.
Statement II: If a raw calculated mean is , it is rounded to to retain 3 significant figures.
Statement III: The sum of and has three significant figures.
Statement IV: When averaging measurements of the same precision, the final result retains the same number of decimal places as the original measurements.
How many of the above statements are correct?
Options
- AOnly three
- BAll four
- COnly two
- DOnly one
Correct answer
A. Only three
Step-by-step solution
Statement I is correct: The count of measurements is an exact number and has infinite significant figures.
Statement II is correct: To retain 3 significant figures in , the digit to be dropped is 5. Since the preceding digit (5) is odd, it is increased by 1, giving .
Statement III is incorrect: According to the rules of significant figures for addition, the result must have the same number of decimal places as the term with the least number of decimal places. . This must be rounded to one decimal place. Since the digit to be dropped is 5 and the preceding digit (6) is even, it is left unchanged. The result is , which has two significant figures, not three.
Statement IV is correct: Since the sum of the measurements retains the same number of decimal places as the original data, and division by an exact integer does not alter this precision, the final average retains the same number of decimal places.
Therefore, exactly three statements (I, II, and IV) are correct.
Answer: Only three
Statement II is correct: To retain 3 significant figures in , the digit to be dropped is 5. Since the preceding digit (5) is odd, it is increased by 1, giving .
Statement III is incorrect: According to the rules of significant figures for addition, the result must have the same number of decimal places as the term with the least number of decimal places. . This must be rounded to one decimal place. Since the digit to be dropped is 5 and the preceding digit (6) is even, it is left unchanged. The result is , which has two significant figures, not three.
Statement IV is correct: Since the sum of the measurements retains the same number of decimal places as the original data, and division by an exact integer does not alter this precision, the final average retains the same number of decimal places.
Therefore, exactly three statements (I, II, and IV) are correct.
Answer: Only three