Q. What are Significant Figures? State the Rules for determining the number of Significant figures:
Answer:
Significant Figure (SF):
In the measurement, the accurate known digits and the first doubtful digit are called Significant figures.
Explanation:
The measurement of physical quantities made by related instruments often involves some errors or uncertainties. These uncertainties are due to the following factors:
(ii) Quality and condition of the apparatus
(iii) Skill of the observer
(iv) Different recorded observations by the same apparatus.
In the presence of these complications, the reported result contains both certain and uncertain digits and the total number of all these certain and uncertain digits are known as significant figures.
Example:
Let the mass of a sphere measured is 1.53 kg. In this case, 1 and 5 are certain digits while 3 is uncertain and the measured value has three significant figures.
Similarly, the length of a simple pendulum measured is 102.5 cm, this value has four significant figures, the digits 1, 0, and 2 are certain while 5 is uncertain.
Rules for determining the number of significant figures:
I. All the non-zero digits (1,2,3,4,5,6,7,8,9) are significant. e.g. 1735 has 4 significant figures.
II. Zero may or may not be significant and it is explained as;
a) All the zeros between two non-zero digits are significant, whether the decimal point exists or does not exist. e.g. 20035, 2.0035, 20.035, in all these cases significant figures are five.
e.g. 6000 Kg can be written as.
6 x 10³ Kg (1 Significant figure)
6.0 x 10³ Kg (2 Significant figures)
6.00 x 10³ Kg (3 Significant figures)
3.040 x 10³ Kg (4 Significant figures)
c) Zero to the right of a non-zero digit in a number without a decimal point is NOT significant. e.g. 2000 has 1 significant figure.
d) When the value is assigned to the measurement (i.e value with fundamental units), it's then counted as SF. e.g. 2000 m has 3 SF.
e) The terminate zero in a number with a decimal point is significant.
e.g. 0.2300, 0.1540, 3.600 All these three numbers have four significant figures each.
d) If the number is less than one, the zero on the right of the decimal point and to the left of the "non zero digits" is not significant, e.g. 0.00123 in this case zeros are not significant and the number of significant figures is three, i.e. 0.00123 = 1.23 x 10⁻³.
III. No change occurs in the number of significant figures by changing the units of the measured value. c.g. 23.15 mm = 2.315 cm = 0.02315 m
All these numbers have four significant figures each.
IV. When two or more measurements are added or subtracted, the result is as precise as the least precise of the quantities. After adding or subtracting, the result should be rounded to the least number of decimal places (DP) as given in the input given number. Some example
+ 23.24 (2DP) - 172.49 (2DP) + 172.49 - 1.3 (1DP)
2378.47 (2DP) 15 427.51 (2DP) 1 5772 (0DP) 12.4 (1DP)
6.9 (2SF) 29.21 (4SF) 10.0 (3SF)
123.1 (4SF) ➗ 23 (2SF) = 5.4 (2SF)
Keep the same number of significant figures as the factor with the least.
(Remember the least S.F in Multiplication or Division)
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