Question

As of july 2013, the population of the united states was$3.164\times {10}^8$ and the national debt was$1.674\times {10}^{13}$ dollars. How much was each person’s share of the debt?

Short answer

Each person debt is$\$5.29\times {10}^4.$

Step-by-step solution

Step 1. Scientific Notation.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

We know that$Eachpersonsharedebt=\frac{Totaldebit}{Totalpopulation}$

Step 2. Determine the expression.

It is given that the population of the United States is $3.164\times {10}^8$

The national debt was.$1.674\times {10}^{13}\text{dollars}$

The required expression is:

$Eachpersondebt=\frac{1.674\times {10}^{13}}{3.164\times {10}^8}$

Step 3. Simplify the expression.

$\begin{array}{l}\frac{1.674\times {10}^{13}}{3.164\times {10}^8}\\ =\frac{1.674}{3.164}\times {10}^{13-8}\\ \approx 0.529\times {10}^5\\ \approx 5.29\times {10}^4\end{array}$

Hence, each person debt is$\$5.29\times {10}^4$.