3 |
Insignificant digit to be dropped is equal to 5 |
If preceding digit is even , it is left unchanged . |
Number – 3.125
Result – 3.12
|
4 |
Insignificant digit to be dropped is equal to 5 |
If preceding digit is odd , it is raised by 1 . |
Number – 3.135
Result – 3.14
|
Rules for determining uncertainty in results of arithmetic calculations To calculate the uncertainty , below process should be used .
o Add a lowest amount of uncertainty in the original numbers . Example uncertainty for 3.2 will be ± 0.1 and for 3.22 will be ± 0.01 . Calculate these in percentage also . o
o
After the calculations , the uncertainties get multiplied / divided / added / subtracted .
Round off the decimal place in the uncertainty to get the final uncertainty result .
Example , for a rectangle , if length l = 16.2 cm and breadth b = 10.1 cm
Then , take l = 16.2 ± 0.1 cm or 16.2 cm ± 0.6 % and breadth = 10.1 ± 0.1 cm or 10.1 cm ± 1 %.
On Multiplication , area = length x breadth = 163.62 cm 2 ± 1.6 % or 163.62 ± 2.6 cm 2 .
Therefore after rounding off , area = 164 ± 3 cm 2 . Hence 3 cm 2 is the uncertainty or the error in estimation . Rules
1 . For a set experimental data of ‘ n ’ significant figures , the result will be valid to ‘ n ’ significant figures or less ( only in case of subtraction ).