Chapter 1, Problem 41A

(a)

To determine

To Calculate: The given operation.

Answer to Problem 41A

  $2.9\times {10}^9{\text{m}}^{\text{2}}$

Explanation of Solution

Given:

  $\left(6.2\times {10}^{18}\text{m}\right)\left(4.7\times {10}^{-10}\text{m}\right)$

Calculation:

  $\begin{array}{c}\left(6.2\times {10}^{18}\text{m}\right)\left(4.7\times {10}^{-10}\text{m}\right)=29.14\times {10}^{18-10}{\text{m}}^{\text{2}}\\ =29.14\times {10}^8{\text{m}}^{\text{2}}\\ =2.9\times {10}^9{\text{m}}^{\text{2}}\end{array}$

It has been rounded off to two significant factors because the least number of significant digits in the number is 2.

Conclusion:

Thus, the result is $2.9\times {10}^9{\text{m}}^{\text{2}}$ .

(b)

To determine

To Calculate: The given operation.

Answer to Problem 41A

  $2.0\times {10}^5\text{m/s}$

Explanation of Solution

Given:

  $\frac{\left(5.6\times {10}^{-7}\text{m}\right)}{\left(2.8\times {10}^{-12}\text{s}\right)}$

Calculation:

  $\begin{array}{c}\frac{\left(5.6\times {10}^{-7}\text{m}\right)}{\left(2.8\times {10}^{-12}\text{s}\right)}=2.0\times {10}^{-7+12}\text{m/s}\\ =2.0\times {10}^5\text{m/s}\end{array}$

It has been rounded off to two significant factors because the least number of significant digits in the number is 2.

Conclusion:

Thus, the result is $2.0\times {10}^5\text{m/s}$ .

(c)

To determine

To Calculate: The given operation.

Answer to Problem 41A

  $1.3\times {10}^{-6}{\text{km}}^{\text{2}}$

Explanation of Solution

Given:

  $\left(8.1\times {10}^{-4}\text{km}\right)\left(1.6\times {10}^{-3}\text{km}\right)$

Calculation:

  $\begin{array}{c}\left(8.1\times {10}^{-4}\text{km}\right)\left(1.6\times {10}^{-3}\text{km}\right)=12.96\times {10}^{-4-3}{\text{km}}^{\text{2}}\\ =12.96\times {10}^{-7}{\text{km}}^{\text{2}}\\ =1.3\times {10}^{-6}{\text{km}}^{\text{2}}\end{array}$

It has been rounded off to two significant factors because the least number of significant digits in the number is 2.

Conclusion:

Thus, the result is $1.3\times {10}^{-6}{\text{km}}^{\text{2}}$ .

(d)

To determine

To Calculate: The given operation.

Answer to Problem 41A

  $1.9\times {10}^2{\text{kg/m}}^3$

Explanation of Solution

Given:

  $\frac{\left(6.5\times {10}^5\text{kg}\right)}{\left(3.4\times {10}^3{\text{m}}^{\text{3}}\right)}$

Calculation:

  $\begin{array}{c}\frac{\left(6.5\times {10}^5\text{kg}\right)}{\left(3.4\times {10}^3{\text{m}}^{\text{3}}\right)}=1.9\times {10}^{5-3}{\text{kg/m}}^3\\ =1.9\times {10}^2{\text{kg/m}}^3\end{array}$

It has been rounded off to two significant factors because the least number of significant digits in the number is 2.

Conclusion:

Thus, the result is $1.9\times {10}^2{\text{kg/m}}^3$ .