All measurements have some degree (quantity) of uncertainty; how great the uncertainty depends on both the accuracy of the measuring device and the skill of its function. For example, on a compass box quantity, the diameter of circle can be calculated to the nearest (least measurement) 0.1 cm; diameter comparison less than this cannot be detected on this scale. We can therefore show the diameter of a cylinder measured on this scale as 15.2 ± 0.1 cm; the ±0.1 is a calculation of the accuracy of the calculation of scale. It is very important to have some shown of how accurately any measurement is made; the ± notation is one way to finished this. It is common to drop the ± notation with the understanding that there is uncertainty of at least one unit in the last digit of the measured quantity; that is, calculated quantities are reported in such a way that only the last digit is uncertain. All of the digits, adding the uncertain one, are known as significant digits or, more commonly, significant rules. The number 2.2 has 2 significant rules, while the value 2.2405 has 5 significant rules.
Rules to determine how many significant numbers has in a measured quantity:
1. All nonzero digits are significant. As like 457 cm has three significant values; 0.25 g has two significant figures.
2. Zeros between nonzero digits are significant. As like, 1005 kg has four significant values; 1.03 cm has three significant values.
3. Zeros to the left of the first nonzero digits in a number are not significant; they merely indicate the position of the decimal point. As like, 0.02g has one significant value; 0.0026 cm has two significant figures.
4. When a number ends in zeros that are to the right of the decimal point, they are significant. As like, 0.0200g has three significant values; 3.0cm has two significant figures.
Exception: When we record the values on actual measurement basis, For example, distance between two city = 1700 km. This number has four significant values.
6. When we change physical quantity from one system to another system, significant numbers are constant. For example, height of tree 1500cm then the number of significant figures remains 2 even if it is represented in meter or kilometre.
7. In exponent (power) form, the exponent term does not contribute to the significant figures. Thus, Planck's constant h = 6.67 ´10-34 J´s which has only three significant figures.
Example:
|
Measured value
|
Number of significant figure
|
Rule
|
|
923912
|
6
|
1
|
|
6024.7
|
5
|
2
|
|
0.09
|
1
|
3
|
|
0.1200
|
4
|
4
|
|
0.01200
|
4
|
4
|
|
4100
|
2
|
5
|
|
1.6 × 10-19
|
2
|
7
|
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