Question

Estimate the number of dentists (a) in San Francisco and (b) in your town or city.

Short answer

The estimated number of dentists in San Francisco is 8000 and in Massachusetts is 6000.

Step-by-step solution

Step 1. Assumptions to determine the order-of-magnitude estimate

To determine the order-of-magnitude estimate of the number of dentists, the following estimates and assumptions are needed:

• The population of the place or city
• The number of patients attended by a dentist in a single day
• The number of working days for a dentist in a year
• The number of times each patient visits the dentist in a year

You may estimate that a dentist attends 10 patients in one day, works 225 days a year, and is visited by each patient twice a year.

Step 2. Determination of the order-of-magnitude estimate

The order-of-magnitude estimate of a physical quantity is the estimate rounded to the nearest power of 10.

1. The population of San Francisco in 2020 was about 8.83 million. So, the estimated population is 9 million.

The number of dentists can be determined as follows:

$\begin{array}{c}N=\left(9\times {10}^6\mathrm{people}\right)\left(\frac{2\frac{\mathrm{visits}}{\mathrm{year}}}{1\mathrm{person}}\right)\left(\frac{1\mathrm{year}}{225\mathrm{working}\mathrm{days}}\right)\left(\frac{1\mathrm{dentist}}{10\frac{\mathrm{visits}}{\mathrm{workday}}}\right)\\ =8000\mathrm{dentists}\end{array}$

Thus, the estimated number of dentists in San Francisco is 8000.

1. The population of Massachusetts (my city) is about 7.1 million. So, the estimated population is 7 million.

The number of dentists can be determined by the method used in part (a).

$\begin{array}{c}N=\left(7\times {10}^6\mathrm{people}\right)\left(\frac{2\frac{\mathrm{visits}}{\mathrm{year}}}{1\mathrm{person}}\right)\left(\frac{1\mathrm{year}}{225\mathrm{working}\mathrm{days}}\right)\left(\frac{1\mathrm{dentist}}{10\frac{\mathrm{visits}}{\mathrm{workday}}}\right)\\ \approx 6222\mathrm{dentists}\end{array}$

Thus, the estimated number of dentists in Massachusetts is 6,000.