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How to find a total from a known percentage

Divide the part by the decimal percentage

If $p$ percent of a whole $N$ equals a known part $a$ , then $(p /100) N = a$ and $N = a / (p /100)$ . Do not multiply by the percentage again; that finds a smaller part instead of the whole.

Problem

In a given year, $23.8%$ of all registered doctors were women. If there were $49, 200$ women doctors, approximately how many registered doctors were there in total? Round to the nearest whole number.

Answer

Approximately

206, 723

doctors.

The percentage is rounded in the source data, so the total is an estimate.

Step-by-step solution

1. Set up the percentage equation

Let $N$ be the total. Since $23.8% = 0.238$ ,

0.238 N = 49, 200.

2. Solve and round

N = \frac{49 , 200}{0.238} \approx 206, 722.689.

Rounded to the nearest whole person, that is $206, 723$ .

3. Check the scale

A part representing less than a quarter of the whole should lead to a whole a little more than four times $49, 200$ . The result fits that expectation.

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