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This is in ArcMap 10.0.

When using data frames to label UTM coordinates, I'm sometimes asked to add leading zeros (e.g., 590 would become 00590) to the tick or line labels of the data frame. I'd like to automate this. I'd be happy using an appropriate style, exporting and editing an attribute table, or editing a shapefile--but I can't figure out how to even access this data outside of ArcMap.

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    I believe the only way to access grids and graticules in ArcMap programmatically is via ArcObjects, not arcpy. How are your programming skills?
    – Fezter
    Jun 14, 2016 at 22:44
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    As @Fezter said, you can access the grid/graticule in ArcObjects but apart from that there's no way to insert leading 0's - except manually, you can convert the labels to annotation then edit them individually; after editing DO NOT CHANGE YOUR EXTENT as the labels will no longer change to match the location. Your best bet is just saying 'no', that can't be done due to software limitations. Jun 14, 2016 at 23:13

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Possible solution:

I created bookmark in layout view and exported it into shapefile. Computed coordinates of 5 points on the left edge using Excel and extent XMin. Labelled them: enter image description here

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