How many multiples of 9 are there in the open interval (π^5, π^6)?

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- Aug 11th 2012, 03:12 AMmusngiburgerCan anyone help me with this one?
How many multiples of 9 are there in the open interval (π^5, π^6)?

- Aug 11th 2012, 06:23 AMSorobanRe: Can anyone help me with this one?
Hello, musngiburger!

Are you waiting for someone to provide a formula?

It is just requires a little*Thinking*.

Quote:

How many multiples of 9 are there in the open interval $\displaystyle (\pi^5,\,\pi^6)\,?$

Use your calculator: .$\displaystyle \begin{Bmatrix}\pi^5 &=& 306.019... \\ \pi^6 &=& 961.389... \end{Bmatrix}$

The interval contains the integers:.$\displaystyle \{307, 308, 309\hdots 961\}$ . . . 655 integers.

One-ninth of them are multiple of 9: .$\displaystyle \left\lfloor \frac{655}{9}\right\rfloor \;=\;72$