Determine the scale factor for three centimeters is equal to 2.7 meters.
Now to begin with, three centimeters is obviously not equal to 2.7 meters. What this question is telling us about is the scale that has been used perhaps for a map or for a model. Three centimeters on the model or the map represents 2.7 meters in real life. We’re asked to determine the scale factor, which means how many times bigger distances are in real life compared to the distances used on the map or the model.
We’ll begin by writing the map or model distance and the real-life distance as a ratio: three centimeters to 2.7 meters. Now, the two parts of this ratio are currently measured in different units: one side is measured in centimeters and the other is measured in meters. In order to determine the scale factor, we need both sides to have the same units.
Now, it doesn’t matter whether I choose to convert both sides of this ratio into centimeters or both sides into meters. I’ll end up with the same result for the scale factor either way. However, if I were to convert three centimeters into meters, then this will give a small decimal value and I prefer to work with integers. For this reason, I’m going to convert both sides into centimeters.
To do so, I need to recall that in one meter, there are 100 centimeters. So in 2.7 meters, there are 270 centimeters. That’s achieved by multiplying 2.7 by 100. Now, I have the ratio three centimeters to 270 centimeters. The units are the same. So they cancel out, leaving a ratio three to 270.
This ratio can be simplified further as both parts have a factor of three. Dividing both parts of the ratio by three gives the simplified ratio one to 90. So the scale factor for the map or model, where three centimeters represents 2.7 meters in reality, is one to 90.
This means that the real-life measurements are 90 times as big as their representations on the map or the model.