Lab Measurements: Significant Figures, Uncertainty, and Dimensional Analysis

Vocabulary flashcards covering significant figures, uncertainty, accuracy vs precision, and dimensional analysis from the lab measurements lecture.

Significant figures (sig figs)

Digits in a measured value that carry meaning about its precision; determine how many digits are considered reliable.

Measured vs exact numbers

Measured numbers come from instruments and have finite sig figs and uncertainties; exact numbers are counted or defined (infinite sig figs).

Leading zeros

Zeros to the left of the first nonzero digit are not significant.

Captive zeros

Zeros between nonzero digits are significant.

Trailing zeros with decimal

Zeros to the right of the last nonzero digit are significant if a decimal point is present.

Trailing zeros without decimal

Zeros at the end of a number with no decimal are ambiguous and often not significant; scientific notation can remove ambiguity.

Scientific notation

Expresses a number as a×10^n with a between 1 and 10; clarifies significant figures and avoids trailing-zero ambiguity.

Exact numbers

Counting numbers or defined quantities (e.g., 1 m = 100 cm, 1000 m in a km) have infinite sig figs.

Precision

How close repeated measurements are to each other (repeatability).

Accuracy

How close a measurement is to the true value; may be accurate, imprecise, or both.

Uncertainty

Doubt associated with a measurement due to instrument quality and technique; every measurement has some uncertainty.

Instrumentation

The quality and capability of the measuring device affecting uncertainty.

Technique

The method used; better technique reduces measurement uncertainty.

Decimal places rule (addition/subtraction)

In addition/subtraction, the result should have as many decimal places as the term with the fewest decimal places.

Significant figures rule (multiplication/division)

In multiplication/division, the result should have as many significant figures as the factor with the fewest sig figs.

Rounding rule

If the next digit is 5 or greater, round up; otherwise round down.

Conversion factor

A ratio that relates two units; used to convert from one unit to another; units cancel out.

Dimensional analysis

A problem-solving framework using conversion factors to cancel units and obtain desired units.

Dimensional analysis grid

A grid or setup to align units top/bottom to ensure proper cancellation when converting units.

Accuracy vs precision visual metaphor

Dartboard/trash can analogy: accuracy is closeness to true value, precision is clustering of results.

Exact conversions in metric system

Conversions within the metric system (e.g., 100 cm = 1 m) are exact and do not limit sig figs.

Example of 0.099 m to inches

To convert, use 100 cm/m and 2.54 cm/in; multiply by appropriate factors and cancel units to obtain inches; keep proper significant figures.

Scientific notation usage for sig figs

Using scientific notation makes the number of sig figs explicit and avoids ambiguity about trailing zeros.