Question

Alice has just discovered base 10 cake! She is delighted with how powerful it is. One day, after nibbling on the cake, Alice realizes she is 1 mile tall. Having her head in the sky makes her think about space travel. She decides she wants to visit the moon, which is about 239,000 miles from the earth. How many more ounces of base 10 cake should Alice eat so the top of her head just touches the moon? Give your answer to the nearest hundredth of an ounce.

Answer 1

5.38 ounces

Explanation:

Given that :

Alice height = 1 mile

Distance of earth to moon = 239000 miles

Number of base 10 cakes required so they Alice's head just touches the moon ;

Using the relation :

Distance = height per ounce * 10^number of ounces

Height per ounce = 1 mile ;

Let number of ounces = n

Hence,

239000 = 1 * 10^n

239000 = 10^n

Take log of both sides

Log(239000) = n

5.3783979 = n

5.3784 = n

Hence, Alice should take 5.38 ounces of base 10 cakes