Question

State the rules for determining the Uncertainty in the Results of Arithmetic Calculations with examples.​

Answer 1

Answer:

Rules for determining uncertainty in results of arithmetic calculations

To calculate the uncertainty, below process should be used.

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.

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 cm2 ± 1.6% or 163.62 ± 2.6 cm2.

Therefore after rounding off, area = 164 ± 3 cm2.

Hence 3 cm2 is the uncertainty or the error in estimation.

Explanation:

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Answer 2

Answer:

To calculate the uncertainty, below process should be used.

(1). Add a lowest amount of uncertainty in the original numbers. ...

(2). After the calculations, the uncertainties get multiplied/divided/added/subtracted.

(3). Round off the decimal place in the uncertainty to get the final uncertainty result.