WEBVTT
00:00:02.160 --> 00:00:07.600
Determine the scale factor for three centimeters is equal to 2.7 meters.
00:00:09.280 --> 00:00:14.100
Now to begin with, three centimeters is obviously not equal to 2.7 meters.
00:00:14.150 --> 00:00:19.900
What this question is telling us about is the scale that has been used perhaps for a map or for a model.
00:00:20.090 --> 00:00:25.450
Three centimeters on the model or the map represents 2.7 meters in real life.
00:00:27.050 --> 00:00:35.980
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.
00:00:37.290 --> 00:00:45.500
We’ll begin by writing the map or model distance and the real-life distance as a ratio: three centimeters to 2.7 meters.
00:00:47.250 --> 00:00:54.990
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.
00:00:55.320 --> 00:00:59.970
In order to determine the scale factor, we need both sides to have the same units.
00:01:01.540 --> 00:01:07.720
Now, it doesn’t matter whether I choose to convert both sides of this ratio into centimeters or both sides into meters.
00:01:07.900 --> 00:01:11.050
I’ll end up with the same result for the scale factor either way.
00:01:12.280 --> 00:01:19.910
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.
00:01:20.320 --> 00:01:23.880
For this reason, I’m going to convert both sides into centimeters.
00:01:25.260 --> 00:01:30.410
To do so, I need to recall that in one meter, there are 100 centimeters.
00:01:32.060 --> 00:01:36.500
So in 2.7 meters, there are 270 centimeters.
00:01:36.680 --> 00:01:40.030
That’s achieved by multiplying 2.7 by 100.
00:01:40.800 --> 00:01:45.530
Now, I have the ratio three centimeters to 270 centimeters.
00:01:46.980 --> 00:01:48.050
The units are the same.
00:01:48.050 --> 00:01:52.220
So they cancel out, leaving a ratio three to 270.
00:01:53.610 --> 00:01:57.710
This ratio can be simplified further as both parts have a factor of three.
00:01:59.270 --> 00:02:05.000
Dividing both parts of the ratio by three gives the simplified ratio one to 90.
00:02:06.940 --> 00:02:15.170
So the scale factor for the map or model, where three centimeters represents 2.7 meters in reality, is one to 90.
00:02:15.670 --> 00:02:22.030
This means that the real-life measurements are 90 times as big as their representations on the map or the model.