It really depends on what you mean by "macro." No zooms are true macro lenses. manufacturers put "macro" on them to indicate that they can focus somewhat closer than normal lenses. To give you an idea, I just took my Tamron 28-75 f/2.8 "macro" to see how close I could get to a quarter. At the closest focus, the quarter filled roughly 1/6 of the viewfinder. (I could have had 3 across, 2 high.) I then put on my EF-s 60mm macro, which is a true macro lens. At closest focus, the portion of a single quarter from just below Washington's chin to the top of the quarter filled the screen.
True macro lenses usually go to 1:1 magnification, meaning that the image on the sensor is life-size, although some cheaper ones only go to 1:2. 1:1 is what most macro photographers would consider a real macro lens.
If you want anything close to 1:1, you either have to buy a real macro lens or do something to a regular lens to get more magnification. One option, suggested above, is to get some extension tubes. This will get you more magnification. However, it makes the viewfinder darker, so if you are starting with a slow lens, it will get pretty dark. The approach has the advantage that if you really get hooked on macro, you can later buy a true macro lens and use the extension tubes with it for even greater magnification.
For example, this was with a 100mm macro lens, I think with no extension:
