Calculate Distance Above Earth's Surface: 1.4x Radius

[Vesper89]

At a certain distance above the surface of the Earth, the graviational force on an object is reduced to 18% of its value at Earth's surface. Determine this distance and express it as a multiple of Earth's radius.

FYI the Earth's mass is 5.98x10^24 kg
and the Earth's radius is 6.38x10^6 m

What I did was this: Gmm/r² = (Gmm/r²)(9/50) The left side is the gravitational force on the object at the surface of the Earth and the right side is %18 of that force (radius is unkown). Since Gmm is constant in both i came up with:

1/r² = 9/50r²
1/6.38x10^6 = 9/50r²
r = 1070m

But I don't understand what they mean in by a multiple of Earth's radius. In the back of my book the answer is 1.4 Re. Is my answer wrong? Or do I just need to take it another step? Thanks for any help!

 

[arildno]

DO NOT PUT IN THOSE MEANINGLESS FIGURES! :grumpy:

Instead:
1. What is meant by a multiple?
In particular: In SYMBOLS, what is a multiple of the Earth's radius?

 

[Vesper89]

I assume its a ratio...in the back of the text the answer is 1.4 Re
(r subscript e...Radius earth) I'm not sure what it means or its significance .

 

[arildno]

What does it mean to multiply?

Do you think that has anything to do with the word "multiple"??