Why is rounding numbers important?

I'll use an example to answer this question...

Suppose you measure the length of your car with a tape measure. Your tape measure shows meters and centimeters.

If your tape measure showed your car as 4 meters and 12 centimeters long and you wanted to convert it to feet google shows the conversion as:

1 meter = 3.2808399 feet

You would find your car is 13.5170604 feet long. Since you could not have possibly found that your car was exactly 3 feet and 1292651/30000000th of an inch it is better to round the number.

In this case, any numbers with greater accuracy than .01 is not only unnecessary, but also unverifiable.