Question:  What do significant numbers mean and how they are determined?

### Significant Numbers

In any measurement, the number of accurately known digits and the first doubtful digit are called significant figures.

#### Rules for finding significant figures

(1) All non-zero digits are significant.

(2) The significance of zero is determined according to the following rules;

1. Zeroes to the left of a sig fig, in simple numbers or decimal fractions, are not significant. For example, 01, 01.2, 0.00651. These numbers have 1, 2 and 3 sig figs, respectively.
2. Zeroes between the sig figs are always significant. Examples 1.205, 10.83
3. In case of decimal fractions, zeroes to the right of a sig fig are always significant. Examples 5.0, 5.30 have 2 and 3 sig figs, respectively.

(3) When the measurement is expressed in scientific notation, all figures before the power of 10 are significant.

(4) The result obtained from addition and subtraction is retained to the least precise measurement in the data.

(5) In the case of multiplication and division, the final result is retained to the measurement that has the least number of sig figs.

Educational Testing and Evaluation Questions

How many significant numbers are in the following measurements?

(a) 12345 cm               (b) 1000 g                    (c) 2500s

(a) 5           (b) 1           (c) 2

Hint: Use Rule (1) and (2).

Find the number of sig figs in the following;

(a) 2005 m         (b) 0.205 g         (c) 0.2050 mL

(a) 4           (b) 3           (c) 4

Find the number of sig figs in the following;

(a) 2000 = 2*103 mm                   (b) 0.050 kg

(c) 50.00 ml                                (d) 0.0250 km

Solution

(a) 1           (b) 2           (c) 4           (d) 3

No of significant figures in 25000 is

(a) 1           (b) 2           (c) 3           (d) 5