Not sure what tool you are using to access those dimensions, but in general, the dimensions shown use the same units that you have selected for the document itself.
To set the units for a single document, turn on your rulers by going to "View" and choosing "Rulers." Then right click on each of the rulers (horizontal and vertical) and change the units to "Percent." Make sure to do it for both rulers.
If you want percent to be the default unit of measurement for all of your documents, you can set it in Preferences.
Hope this solves your problem--if I could figure out how to replicate your document and show the measurements for myself, I would have tested it to make sure.
Merged 2nd answer
Hmm...so grabbed your image to test it. Ignore the magenta lines and percentage values--they aren't from my computer, but are part of your saved image. I used the selection tool and the info panel and tested things on my system, and it seems to figure the percentages correctly. BTW, as part of my test, I determined that Photoshop bases the percentages on the canvas size.
Take a look. In the first image, I selected the entire canvas/image size (they are the same for this image). The info panel shows that the selection encapsulates 100% of the width and height of the image.
In the second image, I selected just the word "Score." The info panel shows what appears to be appropriate percentages compared to the total canvas/image width and height, which is what I think you were trying to determine.
Maybe you can try the same process on your computer and see if your results are similar to mine, and if so, then you might be able to achieve what you want using the info panel. If you get very different results, then I suggest recreating your image in a new Photoshop document to try and eliminate any unusual settings in your current document.
The only other thing I can think of is that you are trying to place the word "Score" a specific percentage from the upper left hand corner of the entire image. If that is the case, then I would just place some guides in the appropriate location on my rulers (which are set to percentages) (i.e. if you want "Score" to be located exactly 33% below the top of the image, place a guide at 33 on your vertical ruler). Then move the word "Score" to the location where the vertical and horizontal rulers cross.
Last, but not least, if you are trying to create a document where the word "Score" only covers a certain percentage of the entire image, then I would suggest using the Histogram feature. This will require some arithmetic on your part, but it is pretty simple. Select the entire image and then look at the histogram. It will show you the total number of pixels selected. Make a note of that number. Then select only the word "Score," and note the total number of pixels selected. Divide the total pixels in "Score" by the pixels for the entire image, and multiply by 100. This will give you the percentage of the entire image encompassed within the selection around the word "Score."
If you are trying to ensure that "Score" is exactly 15% of the entire image, you can find 15% of the total number of pixels, and then resize "Score" so that it matches that number of pixels.
Hopefully something that I said above can help you solve your problem. I hope so.