1.4 Significant Figures

This section describes some of the fundamental laboratory and mathematical skills you will need to be successful in your chemistry course.  For some of you, this discussion will serve as a review, whereas others may be encountering at least some of the ideas and techniques for the first time.

Measurement

Instruments of Measurement

Figure 1.12 Graduated glasswareis used to deliver variable volumes of liquid.

Figure 1.13. Volumetric glasswareis used to deliver (pipette) or contain (volumetric flask) a single volume accurately when filled to the calibration mark

Figure 1.14. A balance is used to measure mass.

A variety of instruments are available for making direct measurements of the macroscopic properties of a chemical substance. For example, we usually measure the volume of a liquid sample with pipettes, burets, graduated cylinders, and volumetric flasks, whereas we usually measure the mass of a solid or liquid substance with a balance. Measurements on an atomic or molecular scale, in contrast, require specialized instrumentation, such as the mass spectrometer.

An exact number results from counting objects or is a part of a definition. For example, 30 students present in class. 30 is the exact number. There are 60 minutes in 1 hour. 60 is the exact number. A measured number results from a measurement or observation and contains some uncertainty also called Inexact number. Limitation of the measuring device and limited powers of the observation of the individual making the measurement involving a degree of uncertainty or error.  That is why measured number are sometimes called approximate number.

Example of exact number: 30 students in class, 12 oranges. Example of measured number: the child weights 30.5 lbs, The height of Mount Everest is 8,848 meters.

Any exact doesn’t have any uncertainty in it. In case of measured number always, the last digit is uncertain. The uncertain number depends on the calibration of the device.

In a measured number always, all digits are certain except the last one. The last digit in a measured number of based on instrumental precision and human eye estimation. It is called uncertain digit or estimated digit.  Certain and uncertain digits together make significant figures.

Watch the following video about certain and uncertain digits.