Absurd prices

Surely you know that supermarkets, shopping centres, and indeed all kind of vendors seem to have fallen in love with the digit $9$, for that digit occurs most often in the price of a product, preferably at the least significant positions. Your favourite chocolate bar might cost $99$ cents, just right to be able to advertise that it costs less than $1$ euro. Your new bicycle might cost $499.98$ euros, which, of course, is less than $500$ euros.

While such comparisons are mathematically sound, they seem to impose a certain amount of stupidity on the customer. Moreover, who wants to carry home those annoying small coins you get back as change?

Fortunately, the FIFA has not adopted this weird pricing scheme: a ticket for the final in the first category for example costs $900$ dollar, in the second category $600$ dollar and in the third category $400$ dollar. These prices may only be regarded weird for other reasons.

We want to distinguish between absurd prices like $99$ cents, $499.98$ euros, etc. and normal prices. To measure the absurdity of a positive integer, do the following:

• Eliminate all trailing zeros, i.e., those in the least significant positions, from the number. You now have a positive integer, say $x$, with a non-zero digit $d$ at its end.

• Count the number of digits, say $a$, of the number $x$.

• if d = 5 the absurdity of the number is 2 \cdot a - 1

• otherwise, the absurdity of the number is 2 \cdot a

For example, the absurdity of $350$ is $3$ and the absurdity of $900900$ is $8$. Using the measure of absurdity, we can define what we call an absurd price: A price $c$ is absurd if and only if the closed interval [0.95 \cdot c, 1.05 \cdot c] contains an integer $e$ such that the absurdity of $e$ is less than the absurdity of $c$.

Given a price in cents, go ahead and tell whether it is absurd!