Question Video: Finding the Scale of a Drawing Given the Real Distance and the Drawing Distance

Given that the distance between two cities on a map is 4.4 cm and the actual distance between them is 26.4 km, what is the drawing scale of the map?

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Video Transcript

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.

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