After her head reaches the moon, Alice continues to enjoy the cake. Eventually her head reaches Pluto, which at the time is approximately 3,670,000,000 miles from the earth. But she forgot to keep track of how many ounces of cake she ate to grow that tall. How many ounces of base 10 beverage must Alice drink to return to a height of 1 mile? Give your answer to the nearest hundredth of an ounce.