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).