Uncertainties (Grade 11)

A set of practice flashcards covering definitions of error and uncertainty, sources and types of errors, absolute uncertainty, how uncertainties combine, and the symbolic problem-solving tip from the notes.

What is error in measurement?

Error = true value − observed value; the difference between the true quantity and what was measured.

List common causes of error in measurement.

Negligence or inexperience; using a faulty apparatus; employing an inappropriate method or technique.

Name the three types of errors mentioned in the notes.

Personal Error, Systematic Error, and Random Error.

What is uncertainty in measurement?

The range of possible values within which the true value lies; a quantitative measure of variability in data.

How should you interpret a measurement like 3.06 mm ± 0.02 mm?

The true value lies between 3.04 mm and 3.08 mm.

What factors contribute to uncertainty?

Limitations of the measuring instrument (systematic error) and the skills of the experimenter.

What is the absolute uncertainty of a measurement?

The least count of the measuring instrument.

If the least count is 1 mm (0.1 cm), how is end uncertainty distributed

Uncertainty develops at each end, typically ±0.05 cm per end (half the least count in cm), leading to a total absolute uncertainty of ±0.1 cm for the measurement.

How are uncertainties combined when adding two measurements?

Absolute uncertainties add; the total uncertainty equals the sum of the end uncertainties.

What is the example given for adding lengths with uncertainty?

Two measurements with ±0.05 cm uncertainty each combine to give a total uncertainty of ±0.1 cm when summed (e.g., (58.0 ± 0.05) cm + (20.5 ± 0.05) cm yields a total uncertainty of ±0.10 cm in the combined length).

What is the recommended approach to solving numerical problems to minimize calculator work?

Solve the problem symbolically (algebraic form) and substitute numerical values only at the end; this allows cancellation and requires rounding only once.

What is the main advantage of using symbolic solutions?

Quantities may cancel during algebraic manipulation, and you round only once on the final result.