Significant Figures - Practice Questions & MCQ

 

• Significant Figures:-

                 The figures of a number that expresses a magnitude to a specified degree of accuracy.

                1) All non zero digits are significant

                   For example-  

                                      42.3 -Three significant figure

                                      238.4 -four significant figure

                                      33.123 -five significant figure

               2) Zero becomes a significant figure if it exists between two non zero digits

                  For example-  

                                     2.09 - Three significant figures 

                                     8.206 -four  significant figures

                                     6.002 -four  significant figures

             3) For leading zero(s), the zero(s) to the left of the first non zero digits are not significant.

                For example-  

                                    0.543 - three   significant figures

                                    0.069 - two  significant figures 

                                    0.002 -one significant figure

             4) The trailing zero(s) in a number without a decimal point are not significant. But if the decimal point is there then they will be counted in significant figures.

                 For example-  

                                  4.330- four  significant figures

                                  433.00- five significant figures

                                  343.000- six   significant figures

             5)  Exponential digits in scientific notation are not significant.

For example-  1.32 X 10^-2 -three significant figures

• Rounding Off:-

Rounding off of figures during calculation helps to make the calculation of big digits easier. While rounding off measurements, we use the following rules by convention:

(1) If the digit to be dropped is less than 5, then the preceding digit is left unchanged.

Example: x=7.82 is rounded off to 7.8, again x=3.94 is rounded off to 3.9.

(2) If the digit to be dropped is more than 5, then the preceding digit is raised by one.

Example : x = 6.87 is rounded off to 6.9, again x = 12.78 is rounded off to 12.8.

(3) If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is raised by one.

Example : x = 16.351 is rounded off to 16.4, again x = 6.758 is rounded off to 6.8.

(4) If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is left unchanged if it is even.

Example : x = 3.250 becomes 3.2 on rounding off, again x = 12.650 becomes 12.6 on rounding off.

(5) If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by one if it is odd.

Example : x = 3.750 is rounded off to 3.8, again x = 16.150 is rounded off to 16.2.

 

Significant Figures in Calculation:-

1. Rules for addition and subtraction-

The result of an addition or subtraction in the number having different precisions should be reported to the same number of decimal places as are present in the number having the least number of decimal places.

For example:-

1) 33.3+3.11+0.313=36.723 but here the answer should be reported to one decimal place as the 33.3 is having the least number of decimal place(i.e only one decimal place), therefore the final answer=36.7

2) 3.1421+0.241+0.09=3.4731 but here the answer should be reported to two decimal places as the 0.09 is having the least number of the decimal place(i.e two decimal places), therefore the final answer=3.47

2 Rules for multiplication and division-

The answer to a multiplication or division is rounded off to the same number of significant figures as is possessed by the least precise term used in the calculation:-

For example:-

1) 142.06 x 0.23=32.6738 but here the least precise term is 0.23 which has only two significant figures, so the answer will be 33.