Cocos (Keeling) Islands is about 12,311 times smaller than Washington.

Washington is approximately 172,348 sq km, while Cocos (Keeling) Islands is approximately 14 sq km, making Cocos (Keeling) Islands 0.01% the size of Washington. Meanwhile, the population of Washington is ~6.7 million people (6.7 million fewer people live in Cocos (Keeling) Islands).
Tip: This to-scale comparison of Washington vs. Cocos (Keeling) Islands uses the Mercator projection, which distorts the size of regions near the poles.