Example 13 from Algebra and Trigonometry, 1.2 Exponents and Scientific Notation

Applying Scientific Notation to Solve Problems

In April 2014, the population of the United States was about 308,000,000 people. The national debt was about $17,547,000,000,000. Write each number in scientific notation, rounding figures to two decimal places, and find the amount of the debt per U.S. citizen. Write the answer in both scientific and standard notations.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The population was $308,000,000 = 3.08 \times 10^{8} .$
The national debt was $$ 17,547,000,000,000 \approx $ 1.75 \times 10^{13} .$
To find the amount of debt per citizen, divide the national debt by the number of citizens.

$\begin{matrix} (1.75 \times 10^{13}) \div (3.08 \times 10^{8}) & = & (\frac{1.75}{3.08}) \cdot (\frac{10^{13}}{10^{8}}) \\ \approx & 0.57 \times 10^{5} \\ = & 5.7 \times 10^{4} \end{matrix}$
The debt per citizen at the time was about $$ 5.7 \times 10^{4},$ or $57,000.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

An average human body contains around 30,000,000,000,000 red blood cells. Each cell measures approximately 0.000008 m long. Write each number in scientific notation and find the total length if the cells were laid end-to-end. Write the answer in both scientific and standard notations.

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solution

Your turn

Solution

Your turn