MEASUREMENT

1.6 -
Significant Figures

1.6.2 - Five Rules for Determining the number of Significant Figures in a Measurement

Why is the measurement "300 L" confusing?

This measurement, as written, ends with zeros but it does not have a decimal point. This leads to confusion because it is not certain whether this measurement is:

• measured using a bucket such that the volume can be anywhere between 250 L to 350 L. In this case, then 300 L has 1 significant figure.
• measured using a measuring device such that the volume is measured to the nearest ten liter, then the measurement is accurate to within 295 L to 305 L. In this case, then 300 L has 2 significant figures.
• measured using a more accurate measuring device such that the volume is measured to the nearest liter, then the measurement is accurate to within 299.5 L to 300.5 L. In this case, then 300 L has 3 significant figures.

To remove the ambiguity associated with any written measurements, we need to be more clear in the way we represent the measurement of "300 L". We can do this in two ways:

• using scientific notation (the recommended way)
• using an overbar to indicate that any figures written to the right of the digit with the overbar is not a significant figure.
 To represent "300 L" as a measurement with Scientific Notation (recommended) Overbar Notation 1 significant figure 3 x 102 L 2 significant figures 3.0 x 102 L 3 significant figures 3.00 x 102 L

Never leave it written as "300 L" !!!