Homework Help: Constructibility of a decimal number

1. Mar 31, 2013

trap101

This a question I have in a number therory course. I've been asked to determine if

3.146891 is constructible.

Since there are probably many ways to solve this I should give a flavor of what I know and maybe then it would be easier to determine the level of detail needed.

So from what I know: a real number is constructible if the point corresponding to it on the number line can be obtained from the marked points 0 and 1 by performing a finite sequence of constructions using only a straightedge and compass.

Another theorem that I feel might be of importance is the fact that if "r" is a positive constructible number, then √r is constructible.

In other examples I used the rational root theroem, but I wasn't dealing with decimals. I just found reading elsewhere that all terminating decimals have a rational representation of the form:

K/ 2n5m.....this was never covered in class, but if this is the case that would mean that 3.146891 is constructible because it is a rational number and I've shown that the rational numbers are consturctible.

Seems long winded in my opinion. Is this the right rationale?

2. Mar 31, 2013

Dick

Of course, it's rational. It's 3146891/1000000.

3. Apr 1, 2013

trap101

hmmmmm. I guess I made a big fuss over nothing then. Thanks.