Christmas Island is about 10,973 times smaller than Alaska.

Alaska is approximately 1,481,348 sq km, while Christmas Island is approximately 135 sq km, making Christmas Island 0.01% the size of Alaska. Meanwhile, the population of Alaska is ~710,231 people (708,026 fewer people live in Christmas Island).
Tip: This to-scale comparison of Alaska vs. Christmas Island uses the Mercator projection, which distorts the size of regions near the poles.