After being dropped a ball always bounces back to \(\frac{2}{9}\) of the height of its previous bounce. After the first bounce it reaches a height of 260 inches. How high will it reach on bounce number 5?

0.63 inches

Explanation

This problem is a series of multiplications by \(\frac{2}{9}\):
\(260 \text { inches } \times \frac{2}{9} \times \frac{2}{9} \times \frac{2}{9} \times \frac{2}{9} = \frac{{260 \times 2 \times 2 \times 2 \times 2}}{{9 \times 9 \times 9 \times 9}} = \frac{{4160}}{{6561}} = 0.63 \text { inches }\)

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