81.

What are the rules for determining the number of significant figures in answers involving:
(i) addition or subtraction
(ii) multiplication or division
(iii) calculations involving a number of steps?

(i) Addition or subtraction. While carrying out addition or subtraction of a number of terms, the result should be reported to the same number of decimal places as that of the term with the least number of decimal places.

(a) Addition of number. Ex. 3·5 g of NaCl and 4·23 g of KCI were dissolved in 25·001 g of water. What is the properly reported mass of solution?
Sol.  +3·5 (this is the term with the least number of decimal place)
                           + 4.23
                           + 25.001
                           _______
Actual sum     = 32.731 g

The respected sum should be only one decimal place after rounding off.

∴  Correct mass of the solution = 32·7 g

(b) Subtraction of number. Ex. Express the result of the following observations to the appropriate number of significant figures: 12·87 – 0·0107.
Sol.  12·87 (this is the term with the least number of decimal place)

      -0.0107
      ________
Actual difference = 12.8693

The reported difference should be only upto two decimal places after rounding off.
∴  Reported difference = 12·87

(ii) Multiplication or division. While carrying out multiplication or division, the number of significant figures in the final result should not exceed the number of significant figures in the least precise factor.

(a) Multiplication of number
Ex. Complete the result of the following calculation to the appropriate number of significant figures:
87·4 × 0·00457
Sol. 87·4 × 0·00457 = 0·399418
As the number of significant figures in the least precise factor is three, therefore the reported result after rounding off is 0·399.

(b) Division of number.
Ex. Express the result of the following calculation to the appropriate number of significant figures:

                  

Sol.            

As the number of significant figures in the least precise factor is two (viz 0·46), therefore the reported result after rounding off is 0·029 (containing only two significant figures).

(iii) Calculations involing a number of steps: If a calculation involves a number of steps, the result should contain the same number of significant figures as that of the least precise number involved other than the exact numbers.