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Take EPS vector ruler and paste it into TIFF image making sure the imported ruler aligns with Illustrators built in rulers to ensure accuracy?

I have an Adobe Illustrator compatible EPS vector file of a measuring ruler in inches. I have a TIFF file that I opened in Adobe Illustrator. When I copy the ruler vector image and drag it into the opened TIFF file I am unable to align the vector image ruler with the artboard ruler in Illustrator. I am using the artboard ruler guides in Illustrator in order to get the correct vector ruler image scaled to the the TIFF image.

I need the ruler embedded on the TIFF image in order to show scale when printing the document.

The result I am getting when long-pressings Shift while expanding the vector ruler image is perfect alignment on the inches but not on the inch increments. For instance, 1 inch and 2 inch and 3 inch etc. are aligned. 1/4 and the subsequent 1/4 are slightly off from each other by less than a pixel but what ends up occurring is the final 1/4 being off by a whole 2 pixels.

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I can't reproduce the problem. I just drew an 10-inch rule, save it as EPS, drag it into a TIF (in Illustrator) and everything looks just fine:

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Perhaps your ruler (EPS) is not accurate enough.

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