Chapter 3, Problem 104A

(a)

To determine

To solve: $6.2\times {10}^{-4}\text{ m + 5}\text{.7}\times {\text{10}}^{-3}\text{ m}$ and express the answer in scientific notation.

Answer to Problem 104A

  $\text{6}\text{.32}\times {\text{10}}^{-3}\text{ m}$

Explanation of Solution

Given:

  $6.2\times {10}^{-4}\text{ m + 5}\text{.7}\times {\text{10}}^{-3}\text{ m}$

Calculation:

  $6.2\times {10}^{-4}\text{ m + 5}\text{.7}\times {\text{10}}^{-3}\text{ m}$

  $\text{= 0}\text{.62}\times {\text{10}}^{-3}\text{ m + 5}\text{.7}\times {\text{10}}^{-3}\text{ m}$

  $\text{= 6}\text{.32}\times {\text{10}}^{-3}\text{ m}$

Conclusion:

  $6.2\times {10}^{-4}\text{ m + 5}\text{.7}\times {\text{10}}^{-3}\text{ m = 6}\text{.32}\times {\text{10}}^{-3}\text{ m}$

(b)

To determine

To solve: $8.7\times {10}^8\text{ km - 3}\text{.4}\times {\text{10}}^7\text{ km}$ and express the answer in scientific notation.

Answer to Problem 104A

  $\text{8}\text{.36}\times {\text{10}}^8\text{ km}$

Explanation of Solution

Given:

  $8.7\times {10}^8\text{ km - 3}\text{.4}\times {\text{10}}^7\text{ km}$

Calculation:

  $8.7\times {10}^8\text{ km - 3}\text{.4}\times {\text{10}}^7\text{ km}$

  $\text{= 8}\text{.7}\times {\text{10}}^8\text{ km - 0}\text{.34}\times {\text{10}}^8\text{ km}$

  $\text{= 8}\text{.36}\times {\text{10}}^8\text{ km}$

Conclusion:

  $8.7\times {10}^8\text{ km - 3}\text{.4}\times {\text{10}}^7\text{ km = 8}\text{.36}\times {\text{10}}^8\text{ km}$

(c)

To determine

To solve: $\left(9.21\times {10}^{-5}\text{ cm}\right)\left(1.83\times {10}^8\text{ cm}\right)$ and express the answer in scientific notation.

Answer to Problem 104A

  $\text{ 1}\text{.685}\times {\text{10}}^4\text{ cm}$

Explanation of Solution

Given:

  $\left(9.21\times {10}^{-5}\text{ cm}\right)\left(1.83\times {10}^8\text{ cm}\right)$

Calculation:

  $\left(9.21\times {10}^{-5}\text{ cm}\right)\left(1.83\times {10}^8\text{ cm}\right)$

  $=\text{16}\text{.85}\times {\text{10}}^3\text{ cm}$

  $\text{= 1}\text{.685}\times {\text{10}}^4\text{ cm}$

Conclusion:

  $\left(9.21\times {10}^{-5}\text{ cm}\right)\left(1.83\times {10}^8\text{ cm}\right)\text{= 1}\text{.685}\times {\text{10}}^4\text{ cm}$

(c)

To determine

To solve: $\frac{2.63\times {10}^{-6}\text{ m}}{4.08\times {10}^6\text{ s}}$ and express the answer in scientific notation.

Answer to Problem 104A

  $6.44\times {10}^{-13}\text{ m/s}$

Explanation of Solution

Calculation:

  $\frac{2.63\times {10}^{-6}\text{ m}}{4.08\times {10}^6\text{ s}}$

  $=6.44\times {10}^{-13}\text{ m/s}$

Conclusion:

  $\frac{2.63\times {10}^{-6}\text{ m}}{4.08\times {10}^6\text{ s}}=6.44\times {10}^{-13}\text{ m/s}$