One thing that hasn't been mentioned here is whether you're planning to update your rear wheel (or at least freehub body) as well. If your bike is all 7-speed, you likely have a 7-speed freehub on the rear wheel, and 8/9/10-speed cassettes are wider than 7-speed cassettes so you'll need to at least update your freehub body in order to fit a 10-speed cassette on the bike.
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"c" is not a unit that measures tire width