Significant digits : All measured quantities have finite precision. Therefore, the number of digits used to write any experimental number should have only that many digits as is warranted by the precision of the particular measurement. The precision depends on the device(s) used as well as the procedure employed.

Q1. Precision and accuracy do not mean the same. What is the difference?

Q2. It is said above, "The precision depends on the device(s) used as well as the procedure employed." Can the same thing be said about accuracy?

In the following arithmatic all numbers represent measured quantities (dimensionless, for convenience!).

Q3. How many significant digits are there in (i) 25.06,  (ii) 367.0,  (iii) 0.0005600 ?

Q4. What is the difference when you say  A = 34., and  A = 34.0?

Q5. k = 0.00065 and k = 0.650E-03 - do these mean the same?

Q6. How do you write 1000 with (i) three significant digits? (ii) four significant digits? (iii) five significant digits?

When we do arithmatic with experimental numbers we shall always take care to round the final result to the correct number of significant digits. Study the following examples:
 

345.45 + 25.789 = 371.24		 12.09 + 0.00079 = 12.09 67. + 346.980 = 414.

2.67 + 345.682 = 348.35		 3467.067 - 3459.8 = 7.3 345. - 7.648 = 337.

 
147. x 4.05 = 595. 347. x 0.406 = 0.141E04 24.6 x 0.0002 = 0.5E-02 296.5/2.75 = 108. 0.04689/34687. = 0.1352E-05

Q7. Can you derive one or more rules for rounding based on the above examples? How do you justify these rules?

Q8. You might have noticed from the examples above that when you take the difference of two nearly equal numbers you lose precision. What procedure will you adopt when you have to take the sum of several positive and negative numbers?

Q9. Simplify:   (i) 34.6 - 34.5 + 28.65 + 346.456 - 245.45
                     (ii)  346.890 / (0.00456 x 4578.)
                    (iii) (47.67 - 48.789) / (456.7899 + 567.99)