Significant Figures and Measuring Instruments

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Let us consider the following entries in a Students' Journal:

(a) Weight of a calorimeter = 42 g

(measuring instrument used is spring balance)

The smallest reading the spring balance can record is 1g.

There are 42 of 1 g units of measurement. Hence, there are two significant figures in the result. The figures are 4 and 2.

(b) The diameter of a bob is measured by (i) the ordinary scale, (ii) the vernier callipers, and (iii) the micrometer.

(i) Diameter = 2.1 cm (measured by the ordinary scale)

The answer has two significant figures.

(ii) Diameter = 2.13 cm (measured by vernier callipers)

The answer has three significant figures.

(iii) Diameter = 2.132 cm (measured by micrometer)

The answer has four significant figures.

The number of significant figures depends on the instrument used and accuracy required.

(c) The exact inner diameter of a test - tube is 2 cm.

(i) The ordinary scale will record 2.0 cm because the least count of the instrument is 0.1 cm.

There are 20 of 0.1 cm units.

(ii) The vernier callipers will record 2.00 cm because the least count of the instrument is 0.01 cm.

There are 200 of 0.01 cm units

The diameter is 2.00 and has 3 s.f.

(iii) The micrometer will record 2.000 cm because the least count of the instrument is 0.001 cm.

There are 2000 of 0.001 cm units.

The diameter is 2.000 cm and has 4 s.f.

(i) It is wrong to record diameter as 2 cm. It means the reading is approximated to the nearest 1 cm. If the exact reading is 2 cm then it should be recorded as 2.0 cm.

(ii) The significant figures express number of units, rounded to the nearest such unit.