Chapter 1, Problem 35A

(a)

To determine

To Solve: The problem and provide correct number of significant figures.

Explanation of Solution

Given: $\text{4}{\text{.667×10}}^{\text{4}}\text{g + 3}{\text{.02×10}}^{\text{5}}\text{g}$

Concept used:

To determine the significant figure in addition, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

Calculations:

  $\begin{array}{l}\text{4}{\text{.667×10}}^{\text{4}}\text{g + 3}{\text{.02×10}}^{\text{5}}\text{g}\\ \text{=34}\text{.867}\times {\text{10}}^4\text{g}\end{array}$

The least number of significant figures is 3. Thus, answer up to three correct significant digits is:

  $\text{=3}\text{.49}\times {\text{10}}^5\text{g}$

Conclusion:

The correct number of significant figures is 3.

(b)

To determine

To Solve: The problem and provide correct number of significant figures.

Explanation of Solution

Given: $\text{1}{\text{.70×10}}^2\text{J }÷\text{3}{\text{.02×10}}^{\text{5}}{\text{cm}}^{-3}$

Concept used:

To determine the significant figure in division, the result must have the exact number of significant figures like the measured value with the least number of significant figures.

Calculations:

  $\begin{array}{l}\text{1}{\text{.70×10}}^2\text{J }÷\text{3}{\text{.02×10}}^{\text{5}}{\text{cm}}^{-3}\\ \text{=0}\text{.5629}\times {\text{10}}^{-3}{\text{J/cm}}^{\text{-3}}\end{array}$

The least number of significant figures is 3. Thus, answer up to three correct significant digits is:

  $\text{5}\text{.63}\times {\text{10}}^{-4}{\text{J/cm}}^{\text{-3}}$

Conclusion:

The correct number of significant figures is 3.