Is space infinately divisable?
Can you keep dividing a unit of measure in half infinately?
If not, what is the smallist space that can be divided into?
If it is, then how can we get anywhere if the distance we have to travel is
always one half way to our destination?

sabrewolfe

Space is infinitely divisble just as numbers are. Take for instance a number line or decimals. .5,.05,.005, etc. You can perpetually add zeros and get smaller fractions of a number just as you could with space itself.
The other part of your question is a bit confusing, but I would like to try and understand it.
What do you mean by not reaching a destination if you are always half way there? Can you elaborate on that?

Capuchin

Space is infinitely divisable, but theoretically the smallest length that it's possible to know anything about is called the Planck Length. Talking about lengths smaller than this is meaningless.

I think you're asking about Zeno's Paradoxes of motion. These paradoxes are very tricky to completely solve to satisfaction today. Something to think about is the sum of an infinite but decreasing series (for example 1/2+1/4+1/8+1/16+...).

Newton1Law

I was under the impression that sapce is not infinately divisible. While measurements to the PLanck scale are extremely small, they are still quantum in nature in that there appears to be a set value for area and volume that we can not go below?? I am no expert on this subject but I find it very interesting.

Consider reading the book, "Three Roads to Quantum Gravity" by Lee Smolin.

DrJ

I bolded the underlying answer in your question.

While it IS infinitely divisible, we certainly don't have the means to measure it.