If you had a mole of U.S. dollar bills and equally distributed the money to all of the people of the world, how rich would every person be? Assume a world population of 7 billion.

In this step, we simply need to find out how many U.S. dollar bills are in a mole. Recall that a mole contains \(6.022\times 10^{23}\) entities. Therefore, a mole of U.S. dollar bills contains \(6.022\times 10^{23}\) U.S. dollar bills.

We need to convert the world population (7 billion) to scientific notation so that we can easily divide it by the mole of U.S. dollar bills. There are two ways to write 7 billion in scientific notation. One way is to write it as \(7\times 10^9\), and the other way is to write it as \(7.0\times 10^9\). In this solution, we will use \(7\times 10^9\).

Now, we need to divide the total amount of money (\(6.022\times 10^{23}\) U.S. dollar bills) by the world population (which we have expressed as \(7\times 10^9\) people), to find out how much money each person would get if the money were distributed equally among them. To do this, we will use the following formula: \[ \text{Money per person} = \frac{\text{Total amount of money}}{\text{Number of people in the world}} \] Plugging in the values, we get: \[ \text{Money per person} = \frac{6.022\times 10^{23}}{7\times 10^9} \] To simplify this expression, first divide \(6.022\) by \(7\), which is approximately \(0.860\). Then, subtract the exponent in the denominator (\(9\)) from the exponent in the numerator (\(23\)), which results in an exponent of \(14\). Therefore, the simplified formula becomes: \[ \text{Money per person} = 0.860\times 10^{14} \]

To convert the final result back to standard notation, we multiply the coefficient (0.860) by \(10^{14}\). Doing this calculation, we get: \[ 0.860\times 10^{14} = 86{,}000{,}000{,}000{,}000 \] So each person would receive $86,000,000,000,000 (86 trillion dollars) if a mole of U.S. dollar bills were distributed equally among the entire global population.