The process of omitting the non significant digits and retaining only the desired number of significant digits, incorporating the required modifications to the last significant digit is called rounding off the number.
In Physics calculation is a vital part and during that we shall reduce the number to the required extend and this is called rounding off and thus we are ready to accept the error up to some extend.
Rules for rounding off numbers:
1. The preceding digit is raised by 1 if the immediate insignificant digit to the dropped is more than 5.
Ex: 4728 is rounded off to three significant figures as 4730.
2. The preceding digit is to be left unchanged if the immediate insignificant digit to be dropped is less than 5.
Ex: 472 is rounded off to three significant figures as 472
3. If the immediate insignificant digit to be dropped is 5 then there will be two different cases
a) If the preceding digit is even, its is to be unchanged and 5 is dropped.
Ex: 4.7258 is to be rounded off to two decimal places. The digit to be dropped here is 5 (along with 8) and the preceding digit 2 is even and hence to be retained as two only
4.7258=4.72
b) If the preceding digit is odd, it is to be raised by 1
Ex: 4.7158 is to be rounded off to two decimal places. As the preceding digit 1 is odd, it is to be raised by 1 as 2.
4.7158=4.72
Rules for Arithmetic Operations with significant Figures:
1. In multiplication or division, the final result should retain only that many significant figures as are there in the original number with the least number of significant figures.
Ex: . But the result should be limited to the least number of significant digits-that is two digits only. So Final answer is 9.9.
2. In addition or substraction the final result should retain only that many decimal places as are there in the number with the least decimal places.
Ex: 2.2+4.08+3.12+6.38=15.78. Finally we should have only one decimal place and hence 15.78 is to be rounded off as 15.8.
In Physics calculation is a vital part and during that we shall reduce the number to the required extend and this is called rounding off and thus we are ready to accept the error up to some extend.
Rules for rounding off numbers:
1. The preceding digit is raised by 1 if the immediate insignificant digit to the dropped is more than 5.
Ex: 4728 is rounded off to three significant figures as 4730.
2. The preceding digit is to be left unchanged if the immediate insignificant digit to be dropped is less than 5.
Ex: 472 is rounded off to three significant figures as 472
3. If the immediate insignificant digit to be dropped is 5 then there will be two different cases
a) If the preceding digit is even, its is to be unchanged and 5 is dropped.
Ex: 4.7258 is to be rounded off to two decimal places. The digit to be dropped here is 5 (along with 8) and the preceding digit 2 is even and hence to be retained as two only
4.7258=4.72
b) If the preceding digit is odd, it is to be raised by 1
Ex: 4.7158 is to be rounded off to two decimal places. As the preceding digit 1 is odd, it is to be raised by 1 as 2.
4.7158=4.72
Rules for Arithmetic Operations with significant Figures:
1. In multiplication or division, the final result should retain only that many significant figures as are there in the original number with the least number of significant figures.
Ex: . But the result should be limited to the least number of significant digits-that is two digits only. So Final answer is 9.9.
2. In addition or substraction the final result should retain only that many decimal places as are there in the number with the least decimal places.
Ex: 2.2+4.08+3.12+6.38=15.78. Finally we should have only one decimal place and hence 15.78 is to be rounded off as 15.8.
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