Significant Figures and Measurement Uncertainty (Vocabulary)

A vocabulary set covering significant figures, measurement uncertainty, and related concepts from the lecture.

Significant Figures

Digits in a measurement that carry meaning about its precision; include all nonzero digits, zeros between nonzero digits, and trailing zeros after a decimal point; leading zeros are not significant.

Uncertainty

The idea that measurements have an inherent error due to instrument limitations, expressed by rounding to reflect precision.

Estimated digit past calibration

An extra digit added to a measurement beyond the smallest scale division to express uncertainty (e.g., 36.5 mL when each division is 0.1 mL).

Nonzero digits

Digits 1–9 that are always significant in a measurement.

Leading zeros

Zeros to the left of the first nonzero digit; not significant (e.g., 0.0123 has three sig figs).

Sandwich zeros

Zeros between nonzero digits; significant.

Trailing zeros with decimal

Zeros to the right of nonzero digits when a decimal point is present; significant.

Trailing zeros without decimal

Zeros at the end of a number without a decimal point; not significant.

Unlimited significant figures

Counted numbers and exact definitions/ratios have unlimited sig figs and do not limit measurement precision.

Mole (mol)

The SI unit for the amount of substance in chemistry.

Counted numbers

Exact counts of objects (e.g., 30 students); have unlimited sig figs.

Scientific notation and sig figs

All digits in the coefficient are significant; the number of sig figs is determined by the digits shown in the coefficient.

Rule for multiplication/division (sig figs)

The result should have as many sig figs as the factor with the fewest sig figs.

Rule for addition/subtraction (sig figs)

The result cannot be more precise than the least precise decimal place among the added/subtracted numbers.

Least precise place value

The decimal place (tenths, hundredths, etc.) that governs how far rounding should go in a calculation.

Accuracy

How close a measurement is to the true or accepted value.

Precision

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

Percent Error

Percent error = |experimental − true| / true × 100; a measure of accuracy.

Experimental value

The value obtained from a measurement in an experiment.