### Video Transcript

The gravitational field strength at
the surface of Earth is 9.8 newtons per kilogram. The gravitational field strength of
the surface of the Moon is 1.6 newtons per kilogram. What is the ratio of the
gravitational field strength at the surface of Earth to the gravitational field
strength at the surface of the Moon? Answer to one decimal place.

Okay, so in this question, we’re
comparing gravitational field strengths at two different locations: one is at the
surface of Earth and the other is at the surface of the Moon. We’re given these strengths in
units of Newtons per kilogram for both of these locations and we want to solve for
their ratio. Specifically, we want to solve for
the ratio of the gravitational field strength of the surface of Earth to the
gravitational field strength of the surface of the Moon. In order to answer this question,
we’ll need to interpret or translate this sentence into a mathematical
expression.

To get started with doing that,
let’s apply some symbols to the terms that we’ve been given. We’re told that the gravitational
field strength at the surface of Earth is a certain value. Let’s call that field strength 𝑔
sub 𝐸. And then likewise, we’ll call the
gravitational field strength at the surface of the Moon 𝑔 sub 𝑀. We’re told that 𝑔 sub 𝐸 is 9.8
newtons per kilogram and 𝑔 sub 𝑀 is 1.6 newtons per kilogram. We want to know the ratio of 𝑔 sub
𝐸 to 𝑔 sub 𝑀.

Now because of the way that these
two terms — the gravitational field strength of the surface of Earth and the field
strength of the surface of the Moon — are arranged in this sentence, we know that
when we go to calculate this ratio, it will be 𝑔 sub 𝐸 divided by 𝑔 sub 𝑀. That’s because we’re finding the
ratio of the field strength on Earth’s surface to that on the Moon’s surface. If the question had instead asked
what is the ratio of the gravitational field strength at the surface of the Moon to
the gravitational field strength at the surface of the Earth, then, in that case, we
would need to reverse these two terms: 𝑔 sub 𝑀 would be on top and 𝑔 sub 𝐸 on
bottom. But with our question written as it
is, 𝑔 sub 𝐸 divided by 𝑔 sub 𝑀 is correct. That’s the ratio we want to solve
for.

And to solve for that ratio, we’ll
divide 9.8 newtons per kilogram by 1.6 newtons per kilogram. Notice by the way, that the units
in these expressions cancel out, as they often do when we calculate a ratio. We’ll end up with a pure
number. And it will be equal to 9.8 divided
by 1.6. When we calculate that fraction, we
find an exact answer of 6.125. But this isn’t our final answer
because we want to give an answer to one decimal place. That means our answer will keep
6.1. And then we’ll round that one up if
the next digit, the two, is greater than or equal to five. But since two is not greater than
or equal to five, we’ll leave the one as it is. To one decimal place then, this is
our answer. The ratio of the gravitational
field strength at the surface of Earth to the gravitational field strength of the
surface of the Moon is 6.1.