MCQ
The numbers $2.745$ and $2.735$ on rounding off to $3$ significant figures will give:
- A$2.75$ and $2.74.$
- B$2.74$ and $2.73.$
- C$2.75$ and $2.73.$
- ✓$2.74$ and $2.74.$
✓
Answer
Correct option: D.
$2.74$ and $2.74.$
Key concept: While rounding off measurements, we use the following rules by convention:
Let us round off $2.745$ to $3$ significant figures.
Here the digit to be dropped is $5,$ then preceding digit is left unchanged, if it is even.
Hence on rounding off $2.745,$ it would be $2.74.$
Now consider $2.737,$ here also the digit to be dropped is $5,$ then the preceding digit is raised by one, if it is odd. Hence on rounding off $2.735$ to $3$ significant figures, it would be $2.74.$
- If the digit to be dropped is less than $5,$ then the preceding digit is left unchanged.
- If the digit to be dropped is more than $5,$ then the preceding digit is raised by one.
- If the digit to be dropped is $5$ followed by digits other than zero, then the preceding digit is raised by one.
- If digit to be dropped is $5$ or $5$ followed by zeros, then preceding digit is left unchanged, if it is even.
- If digit to be dropped is $5$ or $5$ followed by zeros, then the preceding digit is raised by one, if it is odd.
Let us round off $2.745$ to $3$ significant figures.
Here the digit to be dropped is $5,$ then preceding digit is left unchanged, if it is even.
Hence on rounding off $2.745,$ it would be $2.74.$
Now consider $2.737,$ here also the digit to be dropped is $5,$ then the preceding digit is raised by one, if it is odd. Hence on rounding off $2.735$ to $3$ significant figures, it would be $2.74.$
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