UNIT # 1 Introduction Objectives Reading 1.1 Metric System 1.2 1.3 Scientific Notation 1.4 Dimensional Analysis 1.5 1.6 1.7 1.8 Problems 1 | 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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