Tutorial 1.5: Part 1

Measuring to the correct number of significant figures.

How should you record the length of this line when measured with the ruler shown?

The division between the marks is 0.1 cm, so we can record an uncertain but reasonable guess to the nearest 0.01 cm.

Imagine 10 marks between 0.2 and 0.3 cm. Each represents 0.01 cm.

These imaginary marks would lead you to guess 0.24 or 0.25 cm. That last digit is known to be uncertain. Recording 0.24 cm would mean that you are confident that the length is somewhere between 0.23 cm and 0.25 cm. Recording 0.25 cm would mean that you are confident that the length is somewhere between 0.24 cm and 0.26 cm. Both would be correct.

Without visible marks, the length shown can be recorded as 0.24 cm or 0.25 cm. The 2 is certain, and the 4 or 5 is a reasonable guess.

How should you record the length of this line when measured with the ruler shown?

The division between the marks is 1 cm, so we can record an uncertain but reasonable guess to the nearest 0.1 cm.

Imagine 10 marks between 1 cm and 2 cm. Each represents 0.1 cm.

The length shown can be recorded as 1.7 cm (meaning it is between 1.6 cm and 1.8 cm). Since the red line is in fact very close to 1.7 cm it is unlikely that the person recording the length would estimate 1.6 cm or 1.8 cm for the length.

Without visible marks, it can still be seen that the length shown should be recorded as 1.7 cm. The 1 is certain, and the 7 is an estimate.

How should you record the length of this line when measured with the ruler shown?

The division between the marks is 10 cm, so we can record an uncertain but reasonable guess to the nearest 1 cm.

Imagine 10 marks between 0 cm and 10 cm. Each represents 1 cm.

The length shown can be recorded as 9 cm (meaning it is between 8 cm and 10 cm), or 10 cm (meaning it is between 9 cm and 11 cm).

Without visible marks, the length shown can be recorded as 9 cm or 10 cm. No digit is certain, and the 9 or 10 is a reasonable guess.