Constructibility of a decimal number

[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/ 2ⁿ5^m...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?

 

[Dick]

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/ 2ⁿ5^m...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?

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

 

[trap101]

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