# Can anyone help me with this one?

• August 11th 2012, 03:12 AM
musngiburger
Can anyone help me with this one?
How many multiples of 9 are there in the open interval (π^5, π^6)?
• August 11th 2012, 06:23 AM
Soroban
Re: 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 $(\pi^5,\,\pi^6)\,?$

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

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

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