Uncertainty in measurements

Example 1 of a length measurement

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. 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, 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.)

Example 2 of a length measurement

The diagram below shows the measurement of the length of the same blue bar using a ruler with 0.1 cm as its finest division.

Using this ruler, the length the blue bar can be recorded to more accuracy, 2.34 cm. In Section 1.6, you will learn that this measurement has 3 significant figures.

Let's analyze this measurement:

1. Upon inspection of the ruler, we observe that the finest division is a 0.1 cm division.
2. We can always make an estimate of a reading to within the finest division. Therefore, this particular ruler is able to provide a reading accuracy to +/- 0.02 cm. (Note: A plus or minus 0.02 cm reading accuracy means that a length measurement using this ruler will contain uncertainty in the second decimal place.)
3. The end of the blue bar is between the 2.3 cm and the 2.4 cm mark. We can estimate that the blue bar exceeds 2.3 cm mark by approximately 0.04 cm.
4. The length measurement is determined to be 2.34 cm.

The digit '2' and '3' are certain figures. The digit '4' is an uncertain figure, or an estimate in the measurement. Therefore, this length measurement has 3 significant figures. (Note: This measurement is accurate to 2.34 +/- 0.02 cm (i.e. 2.34 plus or minus 0.02 cm). It means that using this ruler, the length of the blue bar is between 2.32 cm to 2.36 cm.)

Content suitability

BCIT courses: CHEM 0011