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Uncertainty in Measurements: Significant Figures, Precision, and Accuracy - Prof. Andy R. , Study notes of Chemistry

The concept of uncertainty in measurements in chemistry, focusing on significant figures, precision, and accuracy. It covers the rules for counting significant figures, significant figure arithmetic, and rounding. Understanding these concepts is crucial for conducting precise and accurate experiments.

What you will learn

  • What are significant figures in chemical measurements?
  • What are the rules for significant figure arithmetic?
  • What is the difference between precision and accuracy in chemical measurements?

Typology: Study notes

2014/2015

Uploaded on 02/02/2015

dantherussky97
dantherussky97 🇺🇸

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Uncertainty in Measurement
In chemistry, we must take measurements from some devices/apparati
(graduated cylinders, burettes, etc.).
When taking these measurements there are certain digits and uncertain
digits.
An uncertain digit is the rightmost digit in a recorded number. Usually only
one recorded.
A measurement always has some degree of uncertainty!
The collection of certain and 1 uncertain digits recorded or used for a
measurement are collectively called the significant figures.
Uncertainty is implied in the rightmost digit to be +/- 1 unless otherwise
noted.
Precision and Accuracy
Although in everyday practice these two words are used interchangeably,
they do mean two different things:
Accuracy – refers to the agreement of a given value to the true value
Precision – refers to the degree of agreement among several measurements
of the same quantity. (Reproducibility of a repeated measurement)
(See dart board example)
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Uncertainty in Measurement

In chemistry, we must take measurements from some devices/apparati (graduated cylinders, burettes, etc.). When taking these measurements there are certain digits and uncertain digits. An uncertain digit is the rightmost digit in a recorded number. Usually only one recorded.

A measurement always has some degree of uncertainty!

The collection of certain and 1 uncertain digits recorded or used for a

measurement are collectively called the significant figures.

Uncertainty is implied in the rightmost digit to be +/- 1 unless otherwise noted. Precision and Accuracy Although in everyday practice these two words are used interchangeably, they do mean two different things:

Accuracy – refers to the agreement of a given value to the true value

Precision – refers to the degree of agreement among several measurements

of the same quantity. (Reproducibility of a repeated measurement) (See dart board example)

Significant Figures and Calculations

Know scientific notation which is sometimes referred to as exponential notation. This is reviewed in Appendix A (pages A-2 and A-3)

I) Rules for Counting Significant Figures

Separate overhead

II) Rules for Significant Figure Arithmetic

Separate overhead

III) Rules for Rounding

  1. In a series of calculations, carry the extra digits through the final result, then round.
  2. If the digit to be removed a) is less than 5, the preceding digit stays the same. An example, 15.22 rounds to? b) is equal to or greater than 5, the preceding digit is increased by 1. An example, 121.45 rounds to?