a piece of ribbon, 25 m long, is cut into pieces of equal length . is it possible to get a piece with irrational length?
When you divide te ribbon into n number of pieces, you get the length of each bit as, 25 / n
where n is any natural number greater than zero.
A rational number is a number that can be expressed as the quotient or fraction p / q of two integers, a numerator p and a non-zero denominator q
25 / n is of the form p / q , so 25 / n is a rational number.
Is not possible to get a piece with irrational length.
please help
To determine if it's possible to get a piece with an irrational length from a 25-meter ribbon cut into pieces of equal length, we need to assess the nature of the cuts.
If the ribbon is cut into a finite number of pieces, it is not possible to obtain a piece with an irrational length. This is because rational numbers, which can be expressed as fractions, represent all possible lengths that can result from a finite number of equal cuts.
However, if the ribbon is cut into an infinite number of pieces, it becomes possible to obtain a piece with an irrational length.
To explain further, let's consider an example. Suppose we cut the ribbon into halves repeatedly. After each cut, the length of the pieces halves, resulting in a sequence like this: 25m, 12.5m, 6.25m, 3.125m, and so on. The length of each piece will eventually approach but never reach zero. By continuing the process infinitely, the length of the pieces will tend towards irrational numbers, such as 2.5m, 1.25m, 0.625m, and so forth.
Therefore, if the ribbon is divided into an infinite number of equal pieces, it is indeed possible to obtain a piece with an irrational length.