Significant figures

Significant figures                                                                              

    Points to understand in significant figures,                                                     

1: Definition with explanation.                                                                                         

    2 : Importance.                                                                                                                   

 3: factors                                                                                                                

4: Rules for measurement of significant figure                                                       

5: Rules for zeroes

1: Definition: in any measurement the accurately known digits including the first doubtful or uncertain digit in the measurement are called significant figures.

Explanation: While doing experiments we facing two types of values, exact and measured. Exact values are those that are counted without ambiguity. For example 6 pencils and 3 books.

 On the other hand numbers which are associated with measurement of any kind are uncertain to an extent.                                                                                                                                                       Suppose we want measure the mass of an object with ordinary physical balance. If the reading in the balance is 7.6 g. In this measurement the first digit 6 after decimal is uncertain. It may be 7.7  or 7.5. It means the reading may be greater than 7.5 and less than 7.7. Or there is uncertainty of measurement is ± 0.1.or 1/10 (there are two significant figures in this measurement)

Similarly if we measure the mass of the same object by more sensitive balance like electrical balance, the reading may be 7.65 grams. In this measurement the first digit 5 is uncertain or doubtful. Or the reading may be greater than 7.64 and less than 7.66. The uncertainty in the measurement is ± 0.01 or 1/100. There are three significant figures in this measurement).              

In the first reading the doubt or uncertainty or error chances was 1/10 while in second reading the uncertainty decreases to 1/100

This shows that with increasing the significant figure decreasing the uncertainty or probability of error.

Importance;

 the number of significant tell us the accuracy of measurement. Greater the number of significant figure more is the accuracy in measurement, For example 10.35 meter length is more accurate reading for a length than 10.3 meter.

Factors.                                                                                                                  

The number of significant figure in a measurement depends on,                                              1; the amount of substance,

2; sensitivity of the instruments                                                                                

General Rules;

 in order to make the decision how many significant figures are to be retained in the final result, we must follow the following rules.                                                                         

  1       all the digits 1,2,3,4,5,6,7,8,9 are significant  figures. e.g in 89.7 mm there are three          digits and all are significant figures.                                                           

2.          In case of zeroes the following rules may be observed,

i)       The zeroes in between two digits are significant zeroes. e.g. 60.8  and 2.06 both have           three significant figures.

ii)      Zeroes at the left of the significant digits are not consider as significant figures. E.g.       0.032 and 0.0032 both have two significant figures. Zeroes are not included in significant       figures. These zeroes are written only for the location of decimal in the measurement.

iii)     Zeroes at the right of the significant figures are considered as significant zeroes like         64.80 and 64.800 have 4 and 5 significant figures respectively. Because the first digit        zero is uncertain, it may be 64.79 or 64.81.                                                          Similarly the second reading may be 64.799       or 64.801.          

iv)     Zeroes at the right of the reading in the exponential form are not considered as     significant zeroes. Like 7.8000 has 5 significant figures but if it is written in 7.80 x 102 form then it has only three significant.

3          Significant figure in multiplication and division;  if we multiply or divide two figure   which have different significant figures. Then the answer must be round of to smaller        number of significant figures.

 

             Example-1                                                                                                                 Multiply 2.5 g x 3.55 g = 8.875                                                                                                           but we will round of to 8.9 g.

Example-2                                                                                                                                        5.348 x 10-2 x 3.64 x 104        = 1.45768982 x 103                                                                           1.336

 

 

As in factor 3.64 x 10 x 104 has three significant figures which is the least number in all the three, therefore the answer should be written to three significant figures only. The answer should be 1.46 x 103.

4          number of significant figures in addition and subtraction;

In adding and subtracting numbers, the numbers of decimal places retained in the answer should be equal to the smallest number of decimal place in any of the quantities being added or subtracted. In this case number of significant figures are not important.it is only the position of the decimal which is important.

 

Examples. Addition of the following quantities in meter.

i)          72.1                            ii) 2.7543                                                                                                           3 .42                               4.10                                                                                                               0.003                            1.273       

            75.523                        8.1273

correct answer for i) is 75.5 m and for ii) is 8.13m.

 

in case of i) the number 72.1 has the smallest decimal place , thus the answer is round off to the position which is then 75.5m.                                                                                                                       in case ii) the number 4.10 has the smallest number of decimal places  and hence the answer is rounded off to the same decimal position which is then 8.13.

Subtraction

Examples

i)               88.9                                         50.5                                                                             - 44.32                                       -3.  2                                                                             44.58                                       47.3                                                                 

correct answers are i) 44.6 and for ii) 47

 

Students  assessment 

MCQs questions for students

1: the accuracy in the measurement is related to significant figures, is such that,

i)          Greater the number of significant figure less will be the accuracy.                                           Ii)            Greater the number of significant figure more will be the accuracy.                                         Iii)     no relation of significant figure with accuracy.                                                                               Iv)      Accuracy and significant figures are inversely proportional.

 

2)         How many significant figures are in the 10.0650 meters                                                                          i)  6                  ii) 5                  iii) 4                 iv) 3                                                                

3)  The number of significant figures in 0.00230300 m is

            i)  6                  ii) 4                  iii) 9                 iv) 8    

4)         The zero digits between two significant figures is

A.   significant

B.   non significant

C.   may not be significant

D.   maybe significant

5)         In the reading 12.7 first two digits are accurate while third one is

A.   accurate

B.   precise

C.   doubtful

D.   correct

 

 

 

 

 

 

 

 

 

 

 

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