You don't need to worry that the print will be smaller.
If you specify 10 cm in Illustrator, it will print as 10 cm, the rulers are accurate.
Your problem is the way Illustrator displays them, Illustrator assumes that there are 72 pixels in an inch, but your display probably has a much higher resolution. A Macbook Pro has a Retina display with a resolution of 220 pixels per inch.
You need to find the correct zoomfactor for your screen to show objects at real size.
If you know the resolution of your display, it is easy to calculate.
Take a MacBook Retina display as an example.
220 ppi is 100%.
1% = 2,2.
72 X 2.2 = 158,4 and that is the zoom percentage that you can enter in the lower left corner of your document window.
There have been several posts about this during the years, one of them suggests measuring your screen to find the zoom percentage.
This one has a script (from Jongware) to zoom.
A Zoom_to script
I modified it to a fixed percentage for a Macbook Retina screen:
// Zoom to 158,4 % Based on script by Jongware: https://forums.adobe.com/thread/832333
// Resolution Retina display 220 ppi. 1% of 220 = 2,2.
// 2,2 X 72 (72 is the default ppi of Illustrator) = 158,4
//
if ( app.documents.length > 0 )
{
app.documents[0].views[0].zoom = 1.584;
}
//