Question

Express the following sum to appropriate number of significant figures :

a. 2.3 × 10³ mL + 4.22 × 10⁴mL + 9.04 × 10³mL + 8.71 × 10⁵mL;

b. 319.5 g – 20460 g – 0.0639 g – 45.642 g – 4.173 g

Answer 1

To perform addition/subtraction operation, first the numbers are written in such a way that they have the same exponent.

The coefficients are then added/subtracted.

(a). (0.23 × 10⁴mL) + (4.22 × 10⁴mL) +(0.904 × 10⁴mL) + (87.1 × 10⁴mL)

= (0.23 + 4.22 + 0.904 + 87.1) × 10⁴mL 

= 92.454 × 10⁴mL 

= 9.2454 × 10⁵ 

= 9.2 × 10⁵mL

(b). 319.5 g – 20460 g – 0.0639 g – 45.642 g – 4.173 g

= – 20190.3789 g 

= – 20190 g

∴ Sum to appropriate number of significant figures = 9.2 × 10⁵mL

Sum to appropriate number of significant figures = – 20190 g

[Note : In addition and subtraction, the final answer is rounded to the minimum number of decimal point of the number taking part in calculation. If there is no decimal point, then the final answer will have no decimal point.]