1.2 Exponents and scientific notation  (Page 7/9)

1. 
   $\begin{array}{cccc}\hfill \left(8.14\times {10}^{\mathrm{-7}}\right)\left(6.5\times {10}^{10}\right)& =& (8.14\times 6.5)\left({10}^{\mathrm{-7}}\times {10}^{10}\right)\hfill & \begin{array}{l}\text{Commutative and associative}\hfill \\ \text{properties of multiplication}\hfill \end{array}\hfill \\ & =& (52.91)\left({10}^3\right)\hfill & \text{Product rule of exponents}\hfill \\ & =& 5.291\times {10}^4\hfill & \text{Scientific notation}\hfill \end{array}$
2. 
   $\begin{array}{cccc}\hfill \left(4\times {10}^5\right)÷\left(\mathrm{-1.52}\times {10}^9\right)& =& \left(\frac{4}{\mathrm{-1.52}}\right)\left(\frac{{10}^5}{{10}^9}\right)\hfill & \begin{array}{l}\text{Commutative and associative}\hfill \\ \text{properties of multiplication}\hfill \end{array}\hfill \\ & \approx & (\mathrm{-2.63})\left({10}^{\mathrm{-4}}\right)\hfill & \text{Quotient rule of exponents}\hfill \\ & =& \mathrm{-2.63}\times {10}^{\mathrm{-4}}\hfill & \text{Scientific notation}\hfill \end{array}$
3. 
   $\begin{array}{cccc}\hfill \left(2.7\times {10}^5\right)\left(6.04\times {10}^{13}\right)& =& (2.7\times 6.04)\left({10}^5\times {10}^{13}\right)\hfill & \begin{array}{l}\text{Commutative and associative}\hfill \\ \text{properties of multiplication}\hfill \end{array}\hfill \\ & =& (16.308)\left({10}^{18}\right)\hfill & \text{Product rule of exponents}\hfill \\ & =& 1.6308\times {10}^{19}\hfill & \text{Scientific notation}\hfill \end{array}$
4. 
   $\begin{array}{cccc}\hfill \left(1.2\times {10}^8\right)÷\left(9.6\times {10}^5\right)& =& \left(\frac{1.2}{9.6}\right)\left(\frac{{10}^8}{{10}^5}\right)\hfill & \begin{array}{l}\text{Commutative and associative}\hfill \\ \text{properties of multiplication}\hfill \end{array}\hfill \\ & =& (0.125)\left({10}^3\right)\hfill & \text{Quotient rule of exponents}\hfill \\ & =& 1.25\times {10}^2\hfill & \text{Scientific notation}\hfill \end{array}$
5. 
   $\begin{array}{ccc}\hfill \left(3.33\times {10}^4\right)\left(\mathrm{-1.05}\times {10}^7\right)\left(5.62\times {10}^5\right)& =& [3.33\times (\mathrm{-1.05})\times 5.62]\left({10}^4\times {10}^7\times {10}^5\right)\hfill \\ & \approx & (\mathrm{-19.65})\left({10}^{16}\right)\hfill \\ & =& \mathrm{-1.965}\times {10}^{17}\hfill \end{array}$

The population was $\mathrm{308,000,000}=3.08\times {10}^8.$

The national debt was $\text{\$}\mathrm{17,547,000,000,000}\approx \text{\$}1.75\times {10}^{13}.$

To find the amount of debt per citizen, divide the national debt by the number of citizens.

The debt per citizen at the time was about $\text{\$}5.7\times {10}^4,$ or $57,000.