Unit #1Unit #2Unit #3Unit #4Unit #5Unit #6Unit #7Unit #8Unit #9Unit #10
spacerUNIT # 1  
spacerspacerIntroduction
spacerspacerObjectives
spacerspacerReading

spacer1.1
Metric
spacerSystem
spacerSI System
spacerBritish System

spacer1.2 Temperature
spacerMeasure-
spacerments

spacer1.3 Scientific
spacerNotation

spacer1.4 Dimensional
spacerAnalysis

spacer1.5 Precision,
spacerAccuracy,
spacerUncertainty

spacerLimitation of the Measuring Instrument
spacerAnalysis of the Limitation of a Ruler
spacerAnalysis of the Limitation of another Ruler
spacer1.6 Significant
spacerFigures

spacerThe Magnitude and Reliability of the Measurement
spacerFive Rules for Determining the number of Significant Figures in a Measurement

spacer1.7 Calculations
spacerInvolving
spacerSignificant
spacerFigures
spacerRules for Rounding off Numbers
spacerRules for Addition  and Subtraction

spacerRules for Multiplication and Division

spacer1.8 Density
spacerDensity and Temperature
spacer1.9 Specific
spacerGravity
spacerspacerProblems
spacer1 | 2 | 3
   

MEASUREMENT

1.6 - Significant Figures


1.6.1 - The Magnitude and Reliability of the Measurement  

Since all experimental measurements have uncertainties, we need to know how much we can trust the measurements. Let's illustrate the idea by considering the mass of an object measured on two different balances. Let's assume that the two balances are accurately calibrated. One measurement is taken on a "crude" balance, and the other is taken on a "sophisticated" balance. The table below shows us how to interpret the two masses.

crude balance sophisticated balance
Measurement
12.4 g
12.4536 g


On a crude balance, we are able to measure to 1 decimal place. On a sophisticated balance, we are able to measure to 4 decimal places. The digits that have no uncertainty are the digits in blue. In other words, the digits that are in blue are the digits that are CERTAIN. The last digit of a measurement that is shown in red always carry an uncertainty due to estimation.

In scientific work, we must always be careful to write down the quantity of measurements properly and to report and calculate quantities that reflect on the accuracy of the measurements. For these reasons, it is important to indicate the margin of error in a measurement by clearly indicating the number of significant figures.

We can determine the number of significant figures for any measurement.

# of sig fig = # of digits that are CERTAIN + 1 final uncertain digit

Points to note:

  • 12.4539 g is a measurement with 6 significant figures. (All digits except for the the final digit '9' are CERTAIN. The final digit '9' is the uncertain digit.)
  • 12.4 g is a measurement with 3 significant figures. (All digits except for the the final digit '4' are CERTAIN. The final digit '4' is the uncertain digit.)

Given that the measuring tool is correctly calibrated, in general, a measurement that has more significant figures is the more accurate or reliable measurement.

Section 2.5
Significant Digits ..p21

 

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