Will be flying in from LAX to Singapore on Air China at Capital Airport with 10hours transit.

Oh, you don't need to apply for a visa. You can enjoy 24 hours visa free policy because your stopover is 10 hours. However, if you wanna tour around downtown area, you need to apply for a Stay Permit at the airport. You can make full use of these 10 hours to go to city center. Wangfujing Area and Tian'anmen Square are highly recommended. Remember to go back to the airport at least 2 hours in advance. :)