A piece of ribbon 25 meters long is cut into pieces of equal length. It is possible to get a piece with irrational length?

nope, each length is 25/2 m which is a rational number.

Nope. If there are n pieces(n an integer), then each piece is 25/n meters long. Since n is an integer, 25/n is a rational number.

To determine whether it is possible to get a piece with an irrational length when a 25-meter ribbon is cut into pieces of equal length, we need to consider the conditions for a length to be rational or irrational.

In mathematics, a rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers. An irrational number, on the other hand, cannot be expressed as a fraction and its decimal representation is non-terminating and non-repeating.

When the ribbon is cut into equal pieces, the length of each piece can be represented as a fraction of 25 meters, where the numerator is the length of the piece and the denominator is the total length of the ribbon.

To determine if it is possible to get a rational or irrational length, we need to examine the factors of the denominator (25) and see if they cancel out with the numerator. If the factors fully cancel out, resulting in a simplified fraction, then the length is rational. If the factors do not fully cancel out, resulting in a fraction that cannot be simplified, then the length is irrational.

Let's examine the factors of 25 (denominator):
1 x 25
5 x 5

Since the factors of 25 do not cancel out with any possible numerator, it is not possible to get a piece with an irrational length. Every piece will have a rational length when the ribbon is divided equally.

Therefore, in this case, it is not possible to get a piece with an irrational length when a 25-meter ribbon is cut into pieces of equal length.

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