Chapter 1.4: Uncertainty in Measurement

Flashcards from Chapter 1.4 of Chemistry: The Molecular Nature of Matter and Change.

Uncertainty

A characteristic of every measurement that results from the inexactness of the measuring device and the need to estimate when taking a reading

• More digits allow for more certainty in measurements

• The rightmost digit is always estimated, always assuming an uncertainty of one unit

Significant figures

The digits obtained in a measurement, signifying greater certainty in a measurement; includes:

• All nonzero digits and zeroes between those digits (502 has 3)

• Trailing zeroes, if the measurement has a decimal point (1.1300 has 5)

• Can be signified in exponential notation by including trailing zeroes

Does not include:

• Leading zeroes (0.00502 has 3)

• Trailing zeroes without a decimal point (6500 has 2, 6500. has 4)

• Can be identified if disappearing in exponential notation

Round-off

What is done to significant figures if there are too many compared to the data

• The least certain measurement sets the limit on calculation certainty and thus determines the number of significant figures in the final answer

  • For multiplication and division, this is for the fewest significant figures

  • For addition and subtraction, this is for the fewest decimal places

Least certain measurement

Sets the limit on calculation certainty and determines the number of significant figures in the final answer

• Multiplication and division use the fewest significant figures

• Addition and subtraction use the fewest decimal places

Use instruments for your necessary level of certainty.

Exact numbers

Numbers with no certainty associated with them, like minutes to hours (60:1) or centimeters to inches (2.54:1)

• These do not limit the number of significant figures in a calculation

Accuracy

The closeness of a measurement to the actual value

• Minimizes systematic error

Precision

The closeness of measurements to each other but not necessarily the actual value

• Minimizes random error

Systematic error

Error producing values that are either all higher or lower than the actual value

• Can be caused by a faulty device or consistent mistakes

• Calibration to a standard can remedy this

Random error

Error producing values that are higher and lower than the actual value

• Always occurs, but depends on skill and instrument precision