Sometimes, one shapefile, supported by Esri, displayed in ArcMap as follow, look at the red line, linear Unit is METER.

And, If you want to read this shapefile to IDL/Matlab, in general, it does not work well with specific functions/routines. Due to its X/Y Coorfinate of entities’vertices, they are in Geodetic Coordinate Style, namely, every vertex coordinate value is not longitude/latitude, look at below in IDL/Matlab,

See above two figures, imagine that these values can’t deliver coordinates correctly. And the result is not what you expect. Let me show it in the tool developed by David W. Fanning.

How to convert Geodetic Coordinate to Geographic Coordinate properly?

Method1, you can change display unit in ArcMap without convertion.

[1]    Start ArcMap, add your shapefile.

[2]   On the table of contents, right click “Layers”. Choose “Properties” form the menu.

[3]   On the “Data Frame Properties”dialog, choose “General” Tab, look at the “Units” area, “Map: Meters” indicates the source map’s unit, shouldn’t be changed at present. Next, “Display: Meters”indicates the ArcMap Window’s unit, one can change to another, set this as below,

Method2, convert to Geographic Coordinate.

[1]    Start ArcMap, add another shapefile, which qualifies the geographic coordinate you want convert to. Look at the red line below,

[2]    Add the shapefile you want to convert.

[3]   On the table of contents, right click the shapefile’s name, choose “Data—Export Data” from the menu.

[4]    On the Export Data dialog, attention,choose “the data frame”, and set the output location, that’s all. Let me see the result below.

Acknowledgements

This work was supported by SHAWNQIAO, KAYSNOWIVY, they both sent their solutions to me by Email. Special thanks to them, and appreciate their contributions and look forward to continued collaboration.