Question

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.)

Answer 1

To compute how much each person in the U.S. would receive from Avogadro's number of pennies, divide 6.022 x 10²23 (Avogadro's number) by 321 million and then convert the result from pennies to dollars. The per capita distribution from Avogadro's pennies is hypothetical and would not reflect actual wealth, unlike the GDP, which measures actual economic output. The $3,500 in circulation per person is not physically carried but held across various institutions.

Step-by-step explanation:

To calculate how much money each person would receive from Avogadro's number of pennies, we need to first understand what Avogadro's number is. Avogadro's number, which is approximately 6.022 x 1023, is the number of units (atoms, molecules, etc.) in one mole of a substance. Considering pennies instead of atoms and dividing this huge number by the U.S. population provides an interesting way to understand the scale of Avogadro's number in terms of currency distribution.

First, let's calculate the number of pennies per person:

1. Divide Avogadro's number by the population of the United States (321 million).
2. The resulting number is the amount of pennies each person would receive.

Now, let's convert the number of pennies to dollars:

1. Since there are 100 pennies in a dollar, divide the number of pennies per person by 100.

As for the comparison with the GDP of the United States, the per capita amount from Avogadro's number of pennies would be a hypothetical figure to illustrate the size of Avogadro's number, whereas the GDP represents the actual economic output of a nation. Comparing the two would show an unrealistic distribution of wealth if it were based solely on Avogadro's number of pennies.

Regarding where the cash is if the total amount of U.S. currency in circulation divided by the population is about $3,500 per person, not all cash is carried by individuals. It is often stored in banks, businesses, and other financial institutions, as part of the transaction processing system, or used in investment and savings programs.