# If I would draw a right triangle with legs of length 1 centimeter with a ruler then its hypotenuse s

If I would draw a right triangle with legs of length 1 centimeter with a ruler then its hypotenuse should be equal to $\sqrt{2}$ which is an irrational number - therefore its decimal representation, which is the limit of the sequence $\underset{n\to \mathrm{\infty }}{lim}\sum _{i=0}^{\mathrm{\infty }}\frac{{a}_{i}}{{10}^{i}}$, has infinitely many numbers after the interger part of$\sqrt{2}$.
What exactly can the ruler measure when drawing such a triangle, considering the fact that we draw irrational number (which by definition is infinitely long)?
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Keegan Barry
If the ruler has marks at 0 cm, 1 cm, 2 cm,... then you will measure that the length of the hypotenuse is between 1 and 2 cm.

If the ruler has marks at 0 mm, 1 mm, 2 mm,... then you will measure that the length of the hypotenuse is between 14 and 15 mm.

So everything depends on where are the marks in the ruler. If it is a special ruler with a mark at $\sqrt{2}$ cm, then it will measure the exact length of the hypotenuse.