Take a circle with a radius of 1cm. Unroll its perimeter and declare that length is 1 of new unit called a squelk.
You can measure things and build things in squelks just fine, but if you try to take something that is 100 squelks long and measure it in centimeters you will get an irrational number of centimeters because there is no rational conversation from squelks to centimeters.
A given length can be irrational in one unit of measure but not in another.
Of course we do have limits of precision in the real world, so in reality nothing lines up quite right.
You can measure things and build things in squelks just fine, but if you try to take something that is 100 squelks long and measure it in centimeters you will get an irrational number of centimeters because there is no rational conversation from squelks to centimeters.
A given length can be irrational in one unit of measure but not in another.
Of course we do have limits of precision in the real world, so in reality nothing lines up quite right.