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

1.5 - Precision, Accuracy and Uncertainty

1.5.2 - Analysis of the Limitation of a Ruler

The diagram below shows the measurement of the length of a blue bar using a ruler with 1 cm as its finest division.

Using this ruler, the length the blue bar is recorded to be 2.3 cm. In Section 1.6, you will learn that this measurement has 2 significant figures.

Let's analyze this measurement:

1. Upon inspection of the ruler, we observe that the finest division is a 1 cm division.
2. We can always make an estimate of a reading to within the finest division. Therefore, to the best of my judgement, I conclude that this particular ruler is able to provide a reading accuracy to +/- 0.2 cm. (Note: A plus or minus 0.2 cm reading accuracy means that a length measurement using this ruler will contain uncertainty in the first decimal place.)
3. The end of the blue bar is between the 2 cm and the 3 cm mark. We can estimate that the blue bar exceeds 2 cm mark by approximately 0.3 cm.
4. The length measurement is determined to be 2.3 cm.
The digit '2' is a certain figure. The digit '3' is an uncertain figure, or an estimate in the measurement. Therefore, this length measurement has 2 significant figures. (Note: This measurement is accurate to 2.3 +/- 0.2 cm (i.e. 2.3 plus or minus 0.2 cm). It means that using this ruler, the length of the blue bar is between 2.1 cm to 2.5 cm.)
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