Question

The area of a national park is 9, 542 square miles. If 14% of the area of the park is reserved for animal preservation, which expression represents the best approximation of the animal preservation area? J) 10,000 • 0.10 K) 10,000 divided by 0.10 L) 10,000 • 0.20 M) 5,000 divided by 0.10 N) 5,000 divided by 0.20

Answer 1

J) 10,000 · 0.10

Explanation:

You want an estimate of the area of a 9542 square mile park reserved for animal preservation if that is 14% of the total area.

Esitmate

We can estimate the area by rounding each of the numbers to 1 significant digit:

9542 ≈ 10,000

14% = 0.14 ≈ 0.10

Then the estimate of the product is ...

9542 · 14% ≈ 10,000 · 0.10 . . . . . matches choice J

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Additional comment

This gives an estimate of 1,000 square miles, which is closer to the actual value of about 1336 square miles than any of the other choices.

A second-order estimate can be had by realizing the park area approximation is about 5% high, and the fraction approximation is about 30% low. Increasing the 1000 square mile estimate by 30% -5% will give about 1250 square miles. This is still somewhat off, but is closer than before. Using better error estimates and error correction will give a better result yet.

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