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Chapter 3: Problem 34

If Avogadro's number of pennies is divided equally among the 321 million men, women, and children in the United States, how many dollars would each receive? How does this compare with the gross domestic product (GDP) of the United States, which was \(\$ 17.419\) trillion in \(2015 ?\) (The GDP is the total market value of the nation's goods and services.)

Short Answer

Expert verified
Each person would receive approximately \(1.875 \times 10^{15}\) dollars. The total amount, \(6.018\times10^{23}\) dollars, is significantly larger than the 2015 US GDP of \(17.419 \times 10^{12}\) dollars. The ratio between the total amount and the GDP is approximately \(3.45 \times 10^{10}\), which means the total amount is approximately 34.5 billion times larger than the 2015 US GDP.

Step by step solution

01

Find the number of pennies per person

Divide Avogadro's number of pennies (\(6.022\times10^{23}\)) by the number of people in the United States (321 million): \[ \text{Pennies per person} = \frac{6.022\times10^{23}}{3.21\times10^8} \]
02

Convert pennies to dollars

Since there are 100 pennies in a dollar, we can convert the number of pennies per person to dollars per person by dividing the above result by 100: \[ \text{Dollars per person} = \frac{\text{Pennies per person}}{100} \]
03

Calculate the total amount in dollars

Now, to find the total amount in dollars, multiply the dollars per person by the number of people (321 million): \[ \text{Total amount in dollars} = \text{Dollars per person} \times 3.21\times10^8 \]
04

Compare the total amount with the US GDP in 2015

Finally, compare the total amount calculated in step 3 with the given GDP of the United States in 2015 which is \(17.419 \times 10^{12}\) dollars: \[ \text{Ratio} = \frac{\text{Total amount in dollars}}{\text{GDP of the United States in 2015}} \]

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