014: Class 11th PHYSICS|Chapter2|Units & Measurement|p9 |JEE |NEET |Board |By S. B. Patel

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NCERT LINE BY LINE SERIES & Deep Dive –Part 9|Class 11|Chapter 2| Units & Measurement |Topic- 2.7.1 Rules for Arithmetic Operations with Significant Figures| 2.7.2 Rounding off the Uncertain Digits |
Brief of the Lecture:
Rules for Arithmetic Operations with Significant Figures
(1) In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
The answer to a multiplication or division is rounded off to the same number of significant figures as possessed by the least precise term used in the calculation.
(2) The result of an addition or subtraction in the number having different precisions should be reported to the same number of decimal places as present in the number having the least number of decimal places.
Rounding off the Uncertain Digits
While rounding off measurements, we use the following rules by convention:
(1) If the digit to be dropped is less than 5, then the preceding digit is left unchanged.
Example : is rounded off to 7.8,
again is rounded off to 3.9.
(2) If the digit to be dropped is more than 5, then the preceding digit is raised by one.
Example : x = 6.87 is rounded off to 6.9,
again x = 12.78 is rounded off to 12.8.
(3) If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is raised by one.
Example : x = 16.351 is rounded off to 16.4,
again x = 6.758 is rounded off to 6.8.
(4) If digit to be dropped is 5 or 5 followed by zeros, then preceding digit is left unchanged, if it is even.
Example : x = 3.250 becomes 3.2 on rounding off,
again x = 12.650 becomes 12.6 on rounding off.
(5) If digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by one, if it is odd.
Example : x = 3.750 is rounded off to 3.8,
again x = 16.150 is rounded off to 16.2.

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