Given that the distance between two
cities on a map is 4.4 centimeters and the actual distance between them is 26.4
kilometers, what is the drawing scale of the map?
So if we think about the
information we’ve been given, we know that we’ve got a map, but we don’t know the
scale of the map. But what we do know is that the
distance between two cities is 4.4 centimeters on the map. And what this represents in real
life is 26.4 kilometers. Well, the first thing we’ll want to
do if we want to work out the scale of the map is get each of our measurements in
the same units. So let’s think of some
conversions. First of all, we know that one
meter is equal to 100 centimeters and one kilometer is equal to 1,000 meters. So therefore, we can say that one
kilometer is gonna be equal to 100,000 centimeters cause we’re gonna get that by
putting those together.
Okay, great. So this is now gonna help us cause
what we can do is convert 26.4 kilometers into centimeters. So therefore, what we can say is
that our scale is gonna be 4.4 centimeters is equal to 2,640,000 centimeters. And we get that because what we do
is multiply 26.4 by 100,000. And when we multiply by 100,000,
then what we do is move each of our digits five place values to the left. So we can see that our two goes
from being a 10 to going to be a million.
Well, if we think about what we get
on the map, typically, we’ll have a scale of one to something. So let’s see if we can do that with
the scale that we’ve got here. But what we’re gonna do then is
divide each side by 4.4. And when we do that, what we’re
gonna get is a scale of one to 600,000. Well, if you think about what
that’s actually going to mean, it means that one centimeter on our map is worth six
kilometers in real life.