--- In

primenumbers@yahoogroups.com, "alden_parent"

<alden_parent@y...> wrote:

> Hi friends,

>

> 21.99113 / 7 = 3.14159 exactly

>

> Is this rational, irrational ??

If you can express it with finite digits and no symbols representing

any other numbers and no trailing......, and it is exact as you say,

it is rational under simple operations.

Your ratio is rather uninspired as pointed out in the previous

response. The trick is to find a ratio of two co-prime integers p/q

that approximates the irrational number to a desired decimal

accuracy . Such a ratio can always be found trivially to whatever

decimal accuracy of you care to (can calculate to). When

approximating an irrational number, there are an infinity of

instances of p/q that differ from the actual number by no more than

1/q, but such a close approximation is not infinitely possible for a

rational number (to make up for this, you get to have the one

instance of exact equality).

-Dick Boland

> It certainly gives to non-transcendental Pi!

> Does it not?