Radiation Pressure Force on Earth

[sharrington3]

Homework Statement

The intensity of sunlight reaching the Earth is $$1360 \frac{W}{m^2}$$.
a.) Assuming all sunlight is absorbed, what is the radiation pressure force on the earth? Give your answer in Newtons. $$F_r=$$
b.) Give your answer as a fraction of the suns gravitational force on the earth. $$\frac{F_r}{F_g}=$$

Homework Equations

Intenisty is given by $$I= \frac{P}{A}$$ where P power and A is the cross sectional area.
Force is given by $$F=\frac{P}{c}=\frac{IA}{c}$$ where c is the speed of light in a vacuum.

The Attempt at a Solution

I solved the first part correctly, no problem. I got that the radiation pressure force was $$5.78*10^8 N$$
For the second part, I simply divided this number by the gravitational force of the sun on the earth, which I found to be $$F_g=3.53*10^{22} N$$
When I divided these two numbers, I got $$\frac{F_r}{F_g}= 1.64*10^{-14}$$ which of course should have no units. However, the problem asks for units, so I put in Newtons anyways, and I was told the my answer must have dimensions of percent (I wasn't aware a unitless quantity had dimensions). So, I slapped in % sign. I was then told to try again; that I was wrong. What am I missing?

 

[mfb]

A fraction of 1 would correspond to 100%. A fraction of 1.64*10¹⁴ corresponds to...?